First, fully charge and load test battery, then, if the battery passes, check charging system output. The alarm is a small draw, but if there is enough time it will drain the battery. The wire for the Tom Tom will only cause a problem only if it is connected to the bike to key off live circuit and left on.
A poor man's load test is to start the bike with a voltmeter across the fully charged battery. If voltage falls below 9.6 V the battery is toast. Not as good as a real load test, but in your case, probably good enough.
A quick test for proper charging is with the voltmeter across the battery and the engine above idle look for 13.5 - 14.5 volts. If you have less, go here:
http://www.electrosport.com/technical-resources/library/diagnosis/fault-finding-guide.php695? Still under warranty?