My previous computer has basically died. And I was wondering if I could transfer all of my steam games onto my new computer? I have re installed steam, and a bunch of my games aren't there to be redownloaded, probably because they were on a free sale.
If you want to download free games you had previously, just search for them in the store and download. Only games that you have bought(or received as gifts) will show up on your games list as uninstalled, free games will never show there but can be downloaded all the same from the store.
Examples of such games: Loadout, Alien Swarm.
I do not recall Steam ever giving out games for free in sales. (There are some games that are free, but those are free forever. You just need to re-find them on the store and redownload them.) Most likely you downloaded the game on a Free Weekend -event. Those games do not work after the weekend, unless you buy the game.
You probably mean free weekend games. They are only tied to your account during the free weekend, then they get removed from your account unless you bought them. All other games are permanently tied to your account.