Not starting!

Hey guys while this thread is open thought I'd toss a question in. I've got a 113 in Ultima 10.2:1 comp. in my '95 fat boy and was getting just a click at the solonoid when I hit the handlebar start button. Sometimes would crank over and other times just click click click. I put a push button on the solonoid and it rolls over every time without fail using a Drag Specialties 310 cca battery. Has been giving me fits starting when cold. Has been in storage over winter and went to get it and was getting erratic spark at the plugs and would not even try to start. Good cranking (sort of) but wouldn't pop. I checked the coil and had 3 ohms primary and like 18,000 secondary and about 12vat coil with ignition on with over 13v at batt. I jumped a wire from batt to coil and the damned thing started right up like it had been running all day. Question is ... where's the best place to look for the problem? Start at the handlebars and work down?
Apologize for the long post but wanted to get all that info in.
Thanks
P.S. I just popped $175 for a 350 cca Big Boar batt. Hope it wasn't just a waste of money.

If jumping past the switches (kill switch, ignition keyswitch) solves the problems, it would seem to be the switches. On my previous bike, (Sportster) I had a case of intermittent starts that I knew was the ignition switch as if I tried it back and forth a few times, it would catch. I changed the switch, and no problems after.

As far as the battery problem that started this thread, verify the voltage at the battery while running as well, highway speeds, not idle. The charging system on bikes is not the same as the one on cars, the voltage regulator on a car adjusts the field current (magnetizing) to maintain a stable voltage. On the bike, (not sure on all bikes, but on most Harleys) they use a permanent magnet rotor (smaller and lighter) so the output voltage increases as RPMs increase, and the big voltage regulator on the front of the frame drops that voltage to the desired 13.8V area. That is also why it has so large a heat sink. If the regulator is failing, it may be too low, or it could get too high at higher RPMs and burn out the battery. Also, in my opinion, some of the chrome regulator covers people like to dress up the bikes with can reduce airflow across the heatsink, and could spell trouble down the road. I advise not using them.

Thanks for the help. I found a questionable jumper wire on the dash ignition switch, cleaned it up and it's been starting good since. There are several jumper wires on the switch and they don't look factory to me. I'm thinking someone put them all around there for a reason but ... what? I'm not good at reading schematics but will maybe call a dealer and ask about all the jumper wires on the switch. Just don't look right to me. There're all red wires with crimp connectors.
At least it starts now and that's always a good thing.
Thanks again
Ride safe

Clean all the connections and make sure there TIGHT! Bad Ground Big Click!

Turns out it was the battery. The shop put it on a load test and no good.
Thanks for all your help.

The first winter I was storing the previous bike, I did not have a tender, so I would start the bike periodically to keep the batter charged. One terminal worked a little loose, and when I went to start it it cranked a little, stopped, and I got a puff of smoke from under the seat. I panicked at first, thinking the wires all melted, but it turned out the battery post melted! I agree, check the connections on a regular basis.