I am trying to get my newly acquired 85 K100 running and I don't think I am getting any spark. I can turn the bike on (headlights, horn, etc..) and it will turn over but will not start. I was reading through other post along with a repair manual and believe the issue is electrical related. Can anyone give me directions on how to test my system?

Go to the portal page and have a look through the electronic ignition troubleshooting page and you should get all you need, well to get the bike going anyway.

So, I charged the battery and hooked it up to see if I could get the bike to start but when I pushed the starter button it only turned over. After I let go of the starter switch it kept trying to start. So, I turned the key off but the bike continued to turn over like it was possessed or something. This kept going till I unhooked the battery. I haven't done anything to the ignition (key switch) or the starter button. The starter button had been broken at some point and the previous owner put a small screw through it but he said that he never had a problem. I let the bike sit for 24 hours and tried it again. NOTHING at all happens but the dash lights and headlight comes on. I can hear a faint click upon pushing the starter but nothing else at all happens.

Battery is not fully charged.
Contacts in the starter get stuck (or something like that) and it just keeps cranking over.

K bikes like all modern cars are quite sensitive to battery condition as in it must be fully charged and in good conditions. Dud or poor battery is one of a few causes of your problem.

I've got the battery on the trickle charger now. I will give it another try tomorrow.

Check the relay is no longer stuck closed otherwise it will start to crank as soon as you touch the second battery terminal onto the battery.
Regards,
K-BIKE