Can I still play Starcraft 1 multiplayer on Battle.Net?
Blizzard has released Starcraft 1 for free. If you download that version (you'll probably need to login into your blizzard account in order to do so), you'll be allowed to login into battle net without any problems.
If you have Windows 9x or Windows XP, perhaps. I haven't been able to play Starcraft 1 for years, simply because I upgraded to Vista (then Win 7) as soon as it came out, and Starcraft 1's DirectDraw suffers massive miscolorization on the newer OS's. The only way I can play is within a tiny window of a virtual machine which I can't handle because my screen resolution is too high so the window is like 3 inches by 3 inches (no I couldn't get it to stretch with the VM software I was trying).