Iphone will not turn on! Shows Apple logo then fades out?

I have an iphone 3g used, jailbroken. Worked fine till last night, left it in car, woke up this morning and was off. I plug it into car charger and now apple logo went on, then fades out and nothing adter 30 seconds. I went to store and guy said to reboot in itunes. I plug it into my computer and NOTHING! Won't detect it or even give the apple screen. I plug it into my car charger, hold home and power button and I get the plug into itunes screen. As soon as i unplug it to connect to laptop itunes, the phone shuts off. Help! My business is on this phone. When it is plugged into i tunes, i just get a faint black screen. I only get apple logo when plugged into car charger.

The battery is dead and may need to be replaced or if it's got liquid damage it may be doing that too. Either way it needs to be fixed at the Apple store.

Apple will not even place a battery in it, they try to sell you a new one. Waste of time get a new phone