I'm trying to log in to my mother's old iMac but she has no idea what the password is anymore. What can I do?

Try the directions in this Apple document: If you forgot your Mac login password

Hi, tslifer65, the answer may be easy, unless she has put on File Vault lock or firmware lock ....but for a simple login/administrator/system password reset, it's a piece of cake (or pie).... this only works with non M1 Macs, as far as I know....the procedure for doing this on M1 Macs is different, and i don't wanna get into that at the moment.....anyways, on to the meat n' potatoes: Restart your mother's old iMac, holding down the Apple/Command/Cloverleaf +R keys on the keyboard until you see a language selection screen. Pick one and continue....from there, move the cursor (the arrow) to the top center of your screen and click. You should see Mac OS X Tools, From there, pick Terminal and continue. Get into Terminal, which should give you a white screen with black letters which is OK for Terminal. Type in "resetpassword" but without the quote marks... Press Enter/Return on your keyboard. This will get you into the main/system/login/administrator password reset application, and you can change that password to whatever you want.... you may want to write it down or use one you can remember.....that's it

John B

Hi, tslifer65, based on the model # you have given me… you have an iMac from late 2012-mid 2017… and the noise description you have given me…. Well, it doesn’t sound too good… you can start off with the basics: reset smc/pmu… run Apple diagnostics… zap pram 4 times on startup… doesn’t look like the later models have an optical ( cd/dvd ) drive so that’s out… that leaves only USB… for #1 and #3 , go here ( link) https://www.macworld.com/article/224955/how-to-reset-a-macs-nvram-pram-and-smc.html… for #2, hold down the “D” key on the keyboard on startup… be patient on that one as it does some basic tests… you should see something on the screen about diagnostics and pass/fail… also see if it’ll do “safe” mode… hold down “shift” key on startup until you see “safe mode” on screen… yup, it’s doing tests… it could be that the internal hard drive (HDD) might have failed….this is not user-serviceable at all… your best bet would be to find and contact an AASP ( apple authorized service provider- where you live) take it into them and see what they have to say…

john B