Download the shop manual from this site, here. There should be information within it to tell you which pins should measure what, on the ECU. You'll need a multimeter that can read Ohms (any multimeter will do this -- you cna buy them through WalMart for less than $20).
This may or may not identify the ECU as bad..... the problem with heat and electronics is that the heat makes electricity flow better through integrated circuits... that makes them fail faster, but is very difficult to observe as they go bad. When they are completely tango uniform, you have a lump of plastic that smells like burnt plastic. On those, all the magic smoke has been let out and there is no going back.
One of the most comprehensive tests you can do is to replace the ECU with a known good one and see if the problem goes away. Not necessarily the cheapest solution out there on a 9 year old bike that is known to have this issue.... probably not a lot of spare ECUs on eBay anymore......
Whatever route you go to correct the problem you have now, if you want to avoid repeating it in the future, you need to make sure the ECU stays as cool as you can. Tucked under the tail, right on top of the hot exhaust with no airflow is one of the worst places Kawasaki could have put the thing, IMHO.
Adding some insulation between the pipe and the ECU will help in the short term, but the thing really needs air flow to cool off.
