Completely dead and unresponsive iPhone

A few days ago my jailbroken iphone 3gs blacked out and would not turn back on. I figured the battery died so I put it on a charger, came back a little while later and it was back on. The next day it blacked out again, this time I knew it was charged so I tried to reset it (power/ home button), and it would not respond. About an hour later I tried reseting it again and it came on. It continued to randomly black out like this a few more times within the next few days and now will not turn back on at all. I left it on the charger for an entire night and day, I just put a brand new battery in it and charged that for an entire day and it still will not turn on or respond at all. After charging it with the new battery the back of the phone was a little warm like it had been charging but it still wont turn on, my computer wont read it, it wont even give me a flashing battery sign. The only thing I can think to relate to this was I updated some software in Cydia a few days before all this started happening, could this be related? Does anyone know how to fix this or have had the same problem? Any help would be greatly appreciated, I am on T-Mobile so I cant just go buy another iPhone without having to sacrifice my kid's collage fund. Thank you all in advance for your time!