Why is my mouse not working on my older iMac?

I have an older Mac that I keep around because I like the old version of Word. It was last used in September. When I turned it on today (March) it

would not recognize the non-mac Bluetooth mouse so I was unable to even get past the startup screen. I changed the batteries turned things on and off and took the Bluetooth connector out of the port a couple of times and tried it in different ports. I then tried my Mac keyboard and mouse that I use with my newer computer. I was able to plug the keyboard directly into the computer so it recognized the keyboard and I was able to use F5 and tabs in order to switch the keyboard to mouse key function but it did not work. I tried several times and every time I opened the menu again mouse keys was already checked as being on but not working. It is not a touch screen so I cannot get past the startup screen and into the computer where I might be able to toggle something to get the mouse working. Thanks for any advice you may have!

[Re-Titled by Moderator]