Ram when bad, will almost always trigger a beep code (if the speaker is connected), as will a lack of video card, which means it's all but certain to be a cpu or mobo fail.
Even if you figure out if it's the cpu or the mobo, you still don't know what caused it to fail or how much damage it did to the other part. It could also be that the PSU over or undervolted, causing damage. The hard drive making noise would indicate a drive failure, but again, that can trace back to the psu, too.
A bad PSU is the scariest.
If the psu goes bad, there's no telling how much in the system is good at this point, and how much re-using them can damage anything you connect to them. My advice would be to get a used mobo off Ebay or a friend that you know is functional and run a good system diagnostic. I wouldn't be surprised if the hard drive fails soon regardless as noise is never good, same for any dvd drives. Motherboards have some voltage protection that drives often lack, so the cpu may be okay which is why I would start with a used mobo you can afford to destroy. If it works, you get off with a used mobo, if it fails, you aren't out a ton of money. I've had two go bad, and I spent weeks chasing down gremlins after.
Basically you have a choice, replace mobo and psu, and hope for the best, possibly chasing gremlins down for weeks or months, or replace pretty much the entire system. That may include video card, unfortunately.
