Hi Moe,
Just a few suggestions you may want to try before buying new parts ('cause they ain't cheap!). One online store I know sells the 12669AS module and they want $48.95. You can get these from time to time on ebay, but its hit and miss whether someone else wants them more than you.
First, make sure the air gap is correct between the module and the flywheel. I don't have the book in front of me, but I think its like .015 - .025" or so. I think I remember someone saying most match books are about the right thickness. I don't smoke, so I usually check the book and use a non-magnetic feeler gauge.
Secondly, if you have a multimeter, test all wires between the module, kill switch, and transformer receptacle to make sure there's no breaks. Also, look for any skinned wires that may be shorting to ground. Fixes here are a lot cheaper than module and transformer replacement.
Third, make sure the kill switch hasn't failed and is shorting to ground. You can do this by simply pulling the wire lead (and make sure its not touching any metal).
If all these steps check out, you may get some idea if the transformer is good with a multimeter. The transformer is just two windings of coil wire, one a primary and one a secondary with a common tie point at one of the connection points. Important things are that neither winding is broken (infinite resistance), and that the windings aren't shorted to each other. If you have a meter that measures resistance, let me know and I'll try to walk you through a test for it.
Best of luck,
Dan