I am sure you could do that. This is not a trivial project and I am sure you could not do it with stock firmware or extra gear.
I think one way you could do that would be to put OpenWRT or DDwrt on the 54gl and set it up to be part of the same SSID as your 600n. You would have to either play games with DHCP assignment of gateways or have special routing tables.
Another option would be for you to install a 802.11g card in your computer and attach to their network. You would probably have to get one or the other network off the 192.168.1.x subnet to make this happen. (I am guessing running a cable to a second NIC in your comp is out of the question as you said wireless.)
You might just be better with an external hard drive for backup.
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