Unless you can find a power supply laying around for free to try you have to decide if you should spend any money at all fixing that. 802.11g stuff is 2 full generations old. You likely could find used 802.11n router if money was a huge issue but even brand new routers are fairly inexpensive.
I have seen people tossing out single band 802.11n routers at the recycle place and they said it still worked so 802.11g is even more trash.