I have seen some strange things attributable to the battery.. including crashing intermittently and rebooting intermittently.. Since your ipod is 3 years old, the battery would be a good first guess. If that doesn't work, then come back and we will figure it out..
Hint: Make sure that whoever you buy your battery from, it is in a SEALED pouch.. Otherwise it could be partially dried out, or a battery that was rejected an an OEM part and sold off as new.. Lots of bogus counterfeit parts out there and the cheaper the part is, usually the more likely it is a sub-standard part. Also, make sure that the battery is for a gen 3 32 or 64gb..