Can you put Steam on a new computer and still keep your account and games

Absolutely! Your Steam account is accessible the same way that an email account is. Once you install Steam on a computer, you can log in with your own account and your entire game library will be available to you. You will need to install whichever games you want to play on the "new" computer, but your account/scores/achievements will all be the same on any computer through the Steam cloud.

I personally have a few games installed on each of my two computers using the same account, and sometimes I log into my friend's Steam program so I can have my achievements there too!