I don't who makes (or more likely, made) that wireless router, but if doesn't support WPA2 now, it probably never did.
Frankly, it's amazing there isn't any information on one of the webpages at least claiming ownership of the intellectual property, a company name, version, etc. You might try backing up the firmware and examining it w/ a hex editor to see if you can perhaps find a string in the embedded software that might reveal a clue.
Even so, my gut tells me it’s time to buy a new router, esp. when they’re dirt cheap. I’ve seen modern wireless N (single stream, 150Mbps) routers for as little as $10-15 lately. Other changes had been made to router technology over the years too, including addressing known vulnerabilities in the Linx kernel/core upon which most of these routers are based.