Just install Steam/HL2 and log in with your steam account and it will work fine. HL2 links itself to your steam account when you install it, so, regardless of where you install it, so long as you log into steam with your HL2 account, it should work fine.
I didn't make it!
Just go to your SAVE folder, and copy and paste them either on to an external HDD(like i did) Or on to a CD.Then open the SAVE folder on your new comp, and paste them there. I did this just 2 days ago.
Ok i think this topic can be closed due to the reasons the problem is already solved , Your face if you have anymore problems with it pm me, Thank you, *closed*