apple mac pro a1186 it chimes on start-up but no display

A1186 looks up to silver tower, original through 2008 models. Do you know what model-year? 2008 models can run 10.11 El Capitan.

a very typical failure is failure of the graphics card, but sub-failures of individual interface have been seen. DO NOT replace like-for-like or you will be right back here too soon. a slight upgrade in technology can provide MUCH more stability.

You can use any monitor. Readers can advise about how to adapt the card outputs to display inputs. Resolutions of most cards will be limited to 2560 by 1600 max.

What MacOS do you/ can you run?

the solid Apple is not in the Mac's ROM at startup. Seeing the solid apple appear says your graphics card supports boot screens, AND the first Blob of software was loaded successfully off the boot drive (that drive appears to be bootable).

at that point the graphics card transitions to its loaded Driver software. what you now appear to have is a row of scrambled dat across the center of the dimply, suggesting that your graphics card was NORT abo=le to make the leap to system Driver.

Safe mode does not use the System driver -- it stays in Boot Screen mode.

do this>> Restart in Safe Mode (by holding Shift as early as possible) and see if you get farther.

Most graphics card require at least one additional "aux" Power cord. The 5770 requires one additional six-pin aux power cord, in addition to the power it draws from being properly plugged into one of the first two PCIe slots.

if you do not have a cord from your old card that you could just move over, Readers can help you find one.

That one, the Apple-firmware 5770 is there best one to install in your circumstances.

The initial "chime" sound is generated in software when your Mac passes the Power-On Self Test. If the chime occurs and/or startup continues, your Mac is working. The screen should light up and draw a blank gray screen. Then on to the Disk Drive.

Accessing the Boot drive:

The solid Apple is not in the Mac's ROM at Cold start. The Apple logo can only appear when it is fetched in the first "blob" of software loaded from a 'magic' place on the boot drive, or re-run after a Restart. Then a whole lot of stuff is initialized, and the progress Bar moves part way across. After a cold start, seeing the solid Apple appear says your drive was able to produce the software that contains the Apple logo.

If a prohibitory sign appears at this point, it indicates some fundamental part of MacOS is damaged or wrong version.

Mounting the Boot drive:

The next step requires a lot of files by name, so the File System is initialized, and the Boot Drive is Mounted. If the drive directory is damaged, the drive can not be Mounted, so your Mac begins one pass of Disk Utility Repair. This will take an additional about five minutes. During this process, the progress bar may be extended, and will grow by an additional amount not seen on a routine startup.

at the end of that process (which should not take more than about five minutes), it will attempt to Mount the drive again:

-- if the drive Mounts, boot-up continues.

-- if the drive cannot be Mounted, your Mac can do nothing more, so it powers off.

I think your graphics card has gone from flaky to failing.

if you have more than one, I think they are BOTH failing.

Overheating will cause sudden emergency uncontrolled power-down, Not what you are reporting.

yes, that is a Mac-Firmware card since it says Apple. it will show boot-up screens. it has DVI-I with VGA alternative, and two Mini DisplayPort outputs.

Drivers for use in running macOS were first available in 10.6.5.

I posted this above:

if you will be running higher than MacOS 10.6.5, good card to install install is a modest-priced used Apple-firmware ATI/AMD 5770 card, which supports one older display on its DVI-I dual-link output (with direct VGA capability there are well, with adapters) AND supports up to two more displays on its two Mini DisplayPort outputs. it requires ONE aux power cable internally, But that is not very difficult to add. Drivers are in MacOS 10.6.5 and later.

Internet Recovery is NOT available in ROM in most Macs before 2011 models. So you will need to explore this list of other possibilities.

When your computer was released, the way you launched the required Utilities (including Disk Utility and Installer) was to use the ones on the Release software DVD. if you have a model-specific version for your model (unlikely) or a Full Retail 10.6 DVD, you use its Utilities, boot and install that version, then use Software update to get to 10.6.8 with all updates, which is the version that can reach out to the Mac App store for the first time and download and install a later version.

10.11 El Capitan is a recommended waypoint, even if you expect to install a later version, because it has an improved Mac App Store that makes getting later versions much easier.

The next source of Utilities is the Recovery Partition on the boot drive. If your drive spins up, even if not MacOS bootable, it may still have a usable recovery partition. To get there, try invoking recovery with Command-R or hold Alt/Option at startup and see if the recovery partition shows as a potentially bootable drive.

Recovery Partitions up through 10.12 Sierra can be found with the Startup Manager (Alt/Option boot). At 10.13, if an SSD boot drive is used, the format is transitioned to APFS. The Recovery partition is present, but it is inside the APFS container, and the Startup Manager on an older Mac may not be able to find it.

The next source of Utilities to consider is any MacOS 10.6 or later versions on any additional drives or clones you may (or may not) have lying about, even if they are from another Mac. You can use those Utilities to ERASE a new drive, and start the installer to place MacOS on the new drive.

The next source to consider is a Time Machine backup drive. Versions from 10.7.3 or later are said to contain a Recovery Partition that could be used to ERASE a new drive and run Installer to place MacOS on a new drive. Time Machine backups created in MacOS 11 Big Sur or later are APFS format, and APFS format backup drives do NOT have a Recovery partition.

Two Mac solutions:

With certain combinations of new and old Mac, you can use Target Disk mode to repair, erase, and install on the drive of the old Mac, by treating it as a disk drive on the new Mac.

Transfer files between two Mac computers using target disk mode - Apple Support

what shows on the display?

-- nothing at all. display card has died

-- flashing question mark. can't find no bootable drive

--- Prohibitory sign (circle with slash) your drive seemed bootable, but very early in the process, a major component was not found, wrong version, or defective

I think your graphics card has gone from flaky to failing.

<did not chime>

The initial "chime" sound is generated in software when your Mac passes the Power-On Self Test. If the chime occurs and/or startup continues, your Mac is working. The screen should light up and draw a blank gray screen.  Then on to the Disk Drive.

if it did Not chime, did the fans spin up?

if the fans spin up, is the power-on indicator blinking a code?

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You need to get to at least 10.9, and then apply all software updates. Then you will be upgraded to Safari 9, which is the oldest Browser that can make an httpS: internet connection today.

this site has direct download links for 10.10 Yosemite and 10.11 El Capitan that do NOT require proper encryption (will work with your installed 10.8)

How to download and install macOS - Apple Support

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