Wireless-g gaming adapter keeps dropping connection

Hello. I'm new to home networking, recently getting broadband (cable)
and sharing it between two wired PCs via a Linksys WRT54G router. I
also have a Playstation2 downstairs that I want to connect to the
Internet. So, I bought the Linksys WGA54G gaming adapter - basically
a bridge - and set it up with no problem.

Now when I'm online with the PS2, I get connection drops all the time.
How can I tell if this is the result of insufficient router range,
bad adapter, or anything else? If it is a range issue (although my
house isn't that that big and the architecture between floors is
pretty open), then what can I do to boost the signal between floors?

Thanks.