1999 Ford Mustang - Special car with a starting issue

I have the SVT ( aka Cobra) version. I love driving it, even to work when weather is good. It has almost 90,000 miles.I have had it for over 10 years. Lately it t has an intermittent starting problem. Two different garages have had it, each over many days to monitor and diagnose. Nothing found wrong. Sometimes when i turn the key it starts, sometimes nothing. The car ‘alarm’ light does not blink, no noise, no dimming of any lights. It starts when i roll it down a hill. At my request these have been replace; starter, ignition switch in column,and the switch when the clutch is depressed that allow the starter to work. On my own i replaced the battery (i had a new Civic once with this problem, the dealer found no problem, i replaced the battery and never had the problem again.) Intermittent starting problem still. ?replace starter relay? Could be a problem with the theft prevention system? Two garages have not found a problem. It has started just fine for them. Changing the battery may have reset something with the disconnect/reconnect?

I Dorothy it is the anti-theft If standard factory system.
If, and it is a big if, there is a fuse that affects ONLY the anti-theft, you could try pulling it and see what happens, of course that might totally disable your Pony.