Ummmm, with that info. we cant really judge.... what is happening. I know the power switch sometimes wears out on the genny 1, 2 of my genny's are worn out like that. Also check the plug itself and all connections. I know ive tossed a genny against a wall and had one fall from atop a book case and down stairs and well had the SHIT beat out of many of em' and damn do they still keep kicking with just minor problems to be fixed like the plug input and power switch.
Those damn game genies break easy though... i remember when i was lil' before the sega cd came out, i plugged my game genie into the expansion port on the side and hooked it to another genny and played a game that way.... HA, smoke, smell, damn and my game genie was fried. Well actually thinking about it now it took quite a bit to fry the lil' fucker, but my genny's lived. HEH. Well to tell you the truth all that happend was the pin for the ground popped on the genie, and the lil pin fell out, so it technically worked, just didnt recognize the fact there was a game in it.