This is called a boot loop. Apple says to do this: Use recovery mode Recovery mode erases your device and restores it, which should resolve the issue. If you previously synced with iTunes or iCloud, you may be able to restore from your backup after recovery. Turn off your device. If you can't turn it off, press and hold the Sleep/Wake and Home buttons at the same time and wait a few seconds for it to turn off. Plug the device's USB cable into your computer only. Hold down the device's Home button as you connect the USB cable to it. When you see the Connect to iTunes screen, release the Home button. If you don't see this screen, try steps 1 through 3 one more time.
You really can't use a Iron on the SMD's. (You can but It needs to have thermal controls). Also capacitors don't blow without a reason. There is a short somewhere else. Probably corrosion bridging a trace. To remove You just need to remove the soldier with wire brade. Re tin the cap you remove and put in place. Heat one side pushing the part down heat the other side. Should be pretty easy.
The logic boards come with the batteries. They are tuned for the cells they are on and can not be swapped because once they are disconnected it will disable the battery. This is why li-ion batteries lose the charge if they sit. The logic board is always active, so it will always be on discharging the battery at 10% per 20-30 day period. The reason for the logic's is a safety thing. If the cells overheat the cells can explode and hurt you. So the charge controller monitors this along with the max amount of charge cycles. Regardless of how many amps are still on the cells it will disable after the factory stated safe charge count.