I think the general consensus we're coming to here is that your computer is an asshole and just doesn't like Half-Life 1. =/
Best suggestion I can give you - aside from what Snesboy already tried - is to completely uninstall the game and ensure all game assets are deleted, then try reinstalling it. Since it's from '98, the download/install from Steam at least shouldn't take all that terribly long.
I'd also suggest re-installing graphics drivers if you haven't, since you mentioned that it played funny with yours.
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