Red should be pos, black neg,white ground/neutral... Check on repair guide to be certain.
I'd start by redoing the solder... PITA but you may have solder joints touching or in the case of your white wire not making clean contact... While the solder is off take a good look with a magnifying lens to check you've got rid of debris and haven't taken off more than you should.
Battery drain may be due to antenna connection, so check the white wires for that are on properly. As you said the drain stopped without the sim this may be a sign it's the problem.
The restarting and reboot loop are battery problems that SHOULD resolve when the battery accepts the charge/stops draining.
Also take a look at the dock connector for dirt and damaged pins that are stooping charge from getting to battery.
You might want to take a look at [http://www.ifixit.com/Answers/View/49224/Replaced+battery+but+phone+now+not+working+and+will+not+turn+on|This post] for great hint on boosting the battery before you reinstall it...
Good luck and let us know how you get on