the wrt54g contains an onboard buck converter, I believe accepting up to 20v and down to 5v, the unit itself running on 3.3v.
have you tried using other power bricks, to see if they have the same problem?
my wrt54g (all three of them) came with heavy unregulated "12vdc" power supplies ... the heft implying a simple transformer + rectifier + cap configuration, leaving the regulation to the chip onboard the wrt
in the field I run my wrt off a parallel bank of 6v gel-cells which fit nicely in a small camera bag, but have also run it straight off "12 volt" power from my truck and a 12v deep-cycle battery, it's a pretty flexible chip
all that being said, if there were something wrong with the chip, it would either not work at all, get terribly hot, smoke something else in the router or all of the above. has any of these symptoms occurred?