Chaos have you purchased Half Life 2, on the account, that you're talking about?
If the answer to this question is "Yes" (as in, Yes, I have played HL2 on this account before), then all you have to do is restart steam. If you have NOT purchased Half-Life 2 on that account, as in you don't own it and haven't played it before, then you need to buy it.
It may very well be a glitch, the same thing happened with almost all of my games yesterday. It said preloading and whenever I tried to play a game it said I needed to buy it, but I'd already bought all of them. I restarted steam and this fixed my problem.
...out of curiosity, why are you asking "restart or purchase" when you could just...take two minutes, TRY restarting and eliminate 50% of your options yourself?