Ssslllooooooowwww Internet

I have an old 700 Mhz eMac with an original AirPort card and 786MB of RAM. I reside at an apartment complex that supplies wireless internet connection to its residents which has worked okay for me until recently. Lately, I've been having connection problems as well as slow download speeds (about 985 kbps according to the most recent result from speedtest.net) My question to you guys is: How do I tell whether the problem lies with the apartment internet antenna or with my old, but beloved eMac? Yeah, I'd like to upgrade to an Intel iMac, but I don't have the cash right now. Should I get my own DSL provider instead of relying on my apartment's system? Any help would be appreciated! Thanks to all in advance! -- Matt