I had the same issue, turns out a 12v wire to the solenoid was not getting full power, here's a copy and paste from my thread when I solved the issue:
Key in, ignition comes on, no warning messages on the dashboard, but the starter motor is not turning the engine over;
1. Check battery, if the lights go dim and you can hear a loud clicking sound as the solenoid tries to kick in, chances are the battery has low charge. Recharge or replace.
2. If the battery is good, can you hear the relay faintly clicking as you push the starter button? (Its under the front seat on up-to 2007 bikes, under the tank on later model hexheads, not sure about twin-cams and toilets).
3. The relay is clicking? Good. To save a lot of time and hassle, do this next: Remove the cover over the starter motor (one screw and pull it back and off).
4. You can now see the thin black wire that goes to the solenoid. Pull it off. Now connect (i.e. just touch) a wire from your battery +ve terminal direct to the spade connector the black wire went to. The starter should now kick into life, and if the ignition is switched on, the bike will start.
5. If you have access to a multimeter, put the +ve probe to the black wire, the -ve to earth. You will probably find that you have much less than 12 volts coming through, which is the cause of your problems.
6. The "official" fix: Go back to the relay, trace where the thick red wire goes to in the loom, find the dodgy connector or broken bit and re-wire/re-attach/re-solder accordingly.
7. The quick fix: Cut the thick red wire that goes to the solenoid. Cover and seal the end that goes back to the loom. Attach a new wire to the end that goes into the relay, fix the other end to the battery +ve. The bike will now start off the button as normal. Sorted!

And don't worry about that red wire being permanently live, the bike won't start without the key in and starter button being pushed. I think its permanently live anyway.
This appears to be a fairly common problem and hopefully you'll now be able to sort it a bit quicker and easier than I did!