Computer has been sitting for over a month without being turned on. When I did, it sounds like it is going to start up, but it does not. Two orange lights come on and a yellow flashes. No Beep sound, but a "turning" sound like something keeps turning over... and not catching. Nothing comes on the screen at all.

The things that turn common to most computers are fans and the hard drive innards. If the computer hiccups like it is starting and then stops, the motherboard or the power supply generally is at fault, however similar behavior can be caused by memory modules or adapters that aren't making good electrical contact with their sockets. This can happen if the computer hasn't been operated for an extended period, has endured temperature swings, or has been moved and jostled. To eliminate this possibility, disconnect the power cord, wait 30 seconds, open the computer, and then remove and reinsert adapters and memory modules. But first, check the light pattern in the computer's documentation which may dictate what the issue is.

I had already removed and reinserted the memory cards before I wrote... but I finally decided to follow your advice and remove them, sprayed them once again with circuit cleaner... let them dry and reinserted them... OMG are you good. The computer started again! Thank you so much for your assistance, you made my day, week, year!

Dusting out the sockets sometimes does the trick too.