bike clicks rapidly, engine does not turn over.

[jdbaum3]

Hello all, I've been lurking for a few months now since we just picked up a GZ for my girlfriend. :popcorn: I finally am at a point that I need some clarification on a few things. I have been searching the forum and it seems others have had similar problems, but never quite the same, and no firm resolutions (yet.) So I thought I'd go ahead and make a thread so I didn't end up hijacking someone else' and keep track of what has and has not been check.
Here is the run down so far, with probably a little excess information thrown in. We picked up the bike a few hundred miles ago and she's been learning to ride on it ever since. The previous owners had put a straight pipe on it and couldn't tell me if the carb had been rejetted for it or not. The bike didn't seem to generate any power, and was as loud as hell :poke2: so I got a used stock exhaust and mounted it up. With the new exhaust it seemed to run much stronger and much quieter :2tup: Kelly continues to ride the bike and picks up the poor habit of inadvertently leaving the bike with the parking light on. The battery is recharged each time with my speed charger at the lowest 2amp setting. I know this is probably too high/fast but it is what I had available and I figured the battery would be replaced shortly anyway :whistle:
So the other day I get a call at work from Kelly telling me she is broken down and can I come get her. I assume it's the light being left on again but she swears that she has been checking and it was not. I didn't have time to look at the bike at all, I just swung by and took her home. The next night I have time to go retrieve the motorcycle. While there I put in the key, all the lights turn on, put it in neutral, check that the kill switch is in the correct position, put the sidestand up, pull in the clutch and try to fire it up. I get a series of clicks, with no sound of life from the engine. There is no audible bogging sound/lights dimming. This isn't how it's behaved before with the battery being too low. The parking lot is slanted, so I wheel it to the top and start pushing it down, figuring I'd try to bumpstart it. I try this several times in both second and third, getting up to 8-10 miles per hour then dropping the clutch. I don't know if I'd have more luck feathering it, but I have always just instantly released the clutch lever when attempting to bump start. Each time the rear wheel instantly locks up, still no sign of the engine trying to turn over. At this point I pop the bike in neutral and push it home. Once home I pull the plug and check for spark while grounding it on the engine. I would get a short spark about 1 in 5 hits of the started, still a rapid clicking noise, sometimes just a single click, but no movement from the engine. :??: So just to take the first step I have recharged the battery and the bike is doing the same thing. I asked Kelly if the bike was running differently at all before she stopped that day and she said there was a new clicking sound when she shifted but couldn't clarify any further than that.
Today I plan on testing the battery and also trying to figure out in the engine is somehow locked up. I saw one recommendation to try wheeling the bike with the spark plug removed in either 4th or 5th gear and the clutch out. Is this the best way to check? :??: If I verify the battery still has enough juice OR replace it and fully charge a new one, what's the next thing to check in the electrical system? :??: I am an electrical dummy, but eager to learn. Sorry, I know this is long, but wanted to be thorough.