iMac won't open user accounts! I have a newer (2009 I believe) iMac, running Yosemite.

It powers on, the Apple logo and progress bar appear, as well as the mouse cursor, but then nothing happens, the screen just stays on and illuminated. Any ideas as to what's up?
it sounds like you never get a logon screen, correct? If so there is likely a problem with the disk, Mac OS or something installed.

First thing to do is to boot up holding the Shift key. When you see the Apple logo you can release it. Now wait for it to boot fully. Safe Mode takes quite a bit longer as it also does some thorough disk checking so be patient.

If you can log in, then do so and start turning off startup items as something that was installed is interfering with the boot process.

If it still does not boot, reboot and hold CommandR to get into recovery mode. run disk utility and reapir the disk, paying attention to any messages that Disk Utility gives you. If it can't repair the disk you can do one of 3 things: erase the HD (losing all files and settings) and reinstall Mac OS. Reinstall Mac OS right over top of what you already have (if it will let you without reformatting the HD) or get another disk repair utility like DiskWarrior and hope that can fix the issue.

If it can repair the disk try booting again. If it finds no problems the Mac OS is likely hosed and needs to be re-installed.