Mmmm .... seems like a case of a busted logic board (the power control chip to be precise). If it is ... the only solution would be swapping the logic board with a new one. And thats not an easy feat. Or u can go kamikaze and solder a wire to bypass the fried chip.

Actually the battery replacement kit is not that expensive. Around USD20 from mobile brando and u can get even cheaper from dealextreme. The real challenge is opening the case. Soldering the battery is not that hard (if u learn those thing in school during kemahiran hidup).