Reboot Randomly

My samsung exhibit 4g running gingerbread 2.3 keeps randomly rebooting. I dont know why but the only way to start it back up is by charging it. or sometimes it will boot up but will says it battery is drained but when i boot it back up plugged in it goes to a battery screen that is almost fully charged. Is it the phone or the battery. i just ordered a new one and i hope its not the phone. does it have anything to do with my 16gb sd card or any apps i have witch ive done a wipe with no apps still does it my battery also is not always tight in the back is that the problem?

Have you tried a hard reset?
I am not sure it will work, but it's worth a try.

1. Turn the power off. If your Samsung Exhibit 4G is frozen, pull the battery out and reinsert it
2. Hold the Volume Down button
3. Press and release the Power button
4. You are now presented with a menu that allows for Fastbook, Recovery, Clear Storage, and Simlock
5. Select Clear Storage by pressing the Volume Down button
6. Press and release the Power button
7. Now simply confirm your decision: Volume Up for YES and Volume Down for NO

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yes i did that but still know difference is it the battery or the phone thanks in advance