I might be able to help a little here, as I have a Yashica MG-1 and an Electro 35GT; I like Yashica rangefinders. Firstly I think Brian's suggestion about the corroded wire is the most likely (more on that later) but I have one thing to suggest which fixed an identical no power problem with my 35GT and battery adapter.
I was skeptical when I read this, but the suggestion is to remove the sticker which indicates polarity from the screw in battery cover. I thought the adapter would still make contact with the metal ring but it didn't. Once the sticker was removed and the glue residue cleaned off, the camera was fine. We should remember that the camera was designed for a much bigger diameter battery with a large flat terminal which wouldn't cause a connection problem. Try this first of all as it requires no dismantling and it might just work.
On to the more likely corrosion theory. I had an Olympus XA which appeared to have only the tiniest smudge of crud leaked from a tiny battery but that was enough to creep up the connecting lead's conductor inside the insulation, eat it all away and ruin the camera, as replacement was impossible due to limited space. The position with your Yashica is much, much better and you should be able to repair a corroded wire. If you remove the bottom cover you will see:
(I've place the battery cover on the right, so that you can see it without its '+' sticker) If the corrosion is in the bottom connection, then there should be plenty of slack in that red wire to enable you to make a repair. I don't know where the other end goes though.
If the corrosion is at the spring end of the battery chamber, then those two screws you can see, hold in the whole battery chamber and you can just slide it out but you will need to remove the camera top cover first to unsolder the far end of the wire that connects to the spring. I've removed the top cover of my MG1, just to clean the rangefinder glass and it's quite easy as there's only the one electrical connection to the hot shoe to disconnect. Removing the advance lever is the only slightly tricky bit.
Here is a photo of another Yashica Electro 35 (which has the same chassis as the MG1) that I have for spares, showing the chamber being slid out.
Don't worry, you won't need to dismantle your camera as far as this, it's just the way may camera is. You only need remove top and bottom covers.
You will need to unsolder the far end of that white wire after removing the top cover to pull out the plastic chamber. You can then replace the whole wire if necessary. My final tip is to make sure that you don't use lead free solder, get some good old fashioned 60/40 stuff which is much easier to melt. Good luck with your camera, it's well worth repairing if you can.
