Can I run Steam games I've purchased on another computer?

Around 2 years ago, my computer kind of shit the bed and I lost all the information on my computer(hard drive was completely fried). Today, I remembered I had GMod on my old computer so I check to see if I can run it. I don’t see any of my games and I was wondering why that was.

My question is this; Since I have a new computer, can I run games I have bought previously on the same steam account but without the old computer? And if not; Is there anything I can do to get them back with buying them again?

Just download them through steam again on your newer system.

That is all.

Install steam on your new computer, log on to your steam account. Double click GMod to start the download.

Edit: …Basically what the above person said