Nano worked only for short while after replacing battery

Symptoms:

- Replaced the battery to my iPod Nano 1st GEN.

- Charged for 7 hours; unplugged and battery was low (red); worked for a very short while.

- Put it back on charge, woke up this morning, iPod Nano kept restarting.

- Last symptom was "Battery very low"; not powering on anymore.

During the battery replacement process I made the following mistakes:

- Burnt the battery's black wire a little with the soldering iron.

- Used soldering iron too much on logic board; soldering areas turned black.

- Didn't clean the areas or properly desolder them.

My question: Can I still fix my Nano if I order a new battery ? I will get it done by a professional (friend) this time.