I see random characters in the game list and in chat, and it doesn't look like an asian language :)
Is there something wrong with my PC?
What you can do is either to change your OS regional settings to use an appropriate language for non-Unicode applications (requires a reboot), or you can try to launch StarCraft through AppLocale, where you can select the language to be used for that particular application. Presumably, the text is supposed to be Korean (because hey, StarCraft), so you'd want to pick that. If you change the OS settings, you probably want to change them back afterwards (so your other non-Unicode applications work as usual).
If you're running Windows XP, you also need to enable support for East Asian languages in the regional settings.
Of course, none of that is strictly necessary to play, and unless you are actually able to read and understand the language, you might as well ignore this display "glitch".