Tom Lee's excellent repair treatise I mentioned above is one source, or you might pick up a copy of Larry Pina's Mac Upgraded and repair. Also the 128K take-apart manual. Search for apple repair manuals online and you will most likely find one you can download. If not, someone on this board surely has a copy they can send you. However, all of the connections in a 128K simply pull apart. Just be careful not to pull so that you impact the neck of the CRT and break it.
The transformer is often that "dirty". It varies from machine to machine. It is not likely the source of any of your problems.
If you are serious about vintage Mac-ing then you should definitely learn how to solder as you will need to do so at some point. It is extremely easy to do and there are many places on the web which instruct you to proper technique.
Whatever you do, DO NOT ALTER an original 128K Mac. The going rate for a 128K in good shape is over $300, clean working ones up to $1,000 depending on accessories. Sell it on eBay before you gut it. Then if you really want a vintage Mac to gut, pick up a cheap Mac Plus or Classic off eBay or Craigslist, which are available in ample quantity, unlike the increasingly rare stock 128K. If you insist on keeping the 128K and gutting it, rather than restoring it, make sure you do not alter the case or parts permanently. There are several threads on this site that will give you links to many well performed mods. Keep everything you remove from the Mac and store carefully. One day you may realize the value of that 128K, even if you do not now, and the value can only increase unless a huge underground cache of pristine 128Ks is discovered over the next 10 years.