Go into your Half-Life folder (Default is C:\SIERRA\Half-Life\) find a folder called auth, delete it. Also in the Half-Life folder there is a file called favsvrs.dat rename it (favsvrs.bak) or delete it ~ I recommend backing it up if you have alot of favorite servers and if you play CS. Then go to START > Find > Files / Folders and search your hard drive for custom.hpk delete all that you find, then search for custom.hp2 and delete all of them aswell.
Reboot and try playing.