Cessna Dude, I'm only 70 years old yet I smell my like burning circuitry when waking up after only a few hours sleep.
Barring an age or moisture induced component failure, I'd rather believe the voltage of your new batteries may be the problem. Maybe properly charged ones are the key to a happy detector/owner relationship.
And, you said the batteries previously removed prior to storage were slightly corroded. Perhaps the battery contacts are still dirty and need a little TLC.
Vintage electronic equipment tends to smell differently when cranked up after sitting a while than our more familiar solid state devices of today.
Believe me, I do have some very vintage electronics, and absolutely adore that smell..along with their robust construction and long life expectancy.
I am not familiar with the type of circuitry used on vintage metal detectors but Radio Shack has a good stock of capacitors and a catalog with many more they don't stock in the stores. Maybe they can help.
Harbor Freight stocks two different, more modern, yet quaintly vintage appearing metal detectors at less than $100.00 apiece.
If nostalgia is the ultimate goal of repairing the Fisher, maybe you should just opt for a new HF detector instead....sorry, that just crept in there.
Seriously, good luck with your metal detector and your future digs.
ATP/GPP/Fiskars Diggers/BH Outback/CT hand held