I have a really nice T-50 which will not trip the shutter. The "P" light comes on in the viewfinder but the shutter won't trip. I'm assuming that a release magnet needs cleaning or something like that. I've had the bottom off but cannot seem to locate the magnet to check it out. Is it under the top cover?
There is no solenoid to be seen either beneath the top-plate or the baseplate. However - the solenoid factor was just your speculation and I suggest another possible cause. The shutter release button compresses three leaf contacts. So you have four contact areas for contamination. I suggest you remove the top-plate. Place some narrow strips of photocopy paper between the contacts; use your finger as the shutter-release button thereby compressing the contacts and then withdraw the paper strips whereby to clean the contact areas. Do it several times. This worked for me on what appeared a dead T50.
I have no doubt repaired several hundred T-50's and almost everyone of them had a cocking and re-cycling problem which can be solved under the bottom plate. Try a couple drops of lighter fluid and a block of wood to help it decide to re-cycle!! I've also had a few that had major corrosion under the top......right above the battery well area. Art @ www.flcamerarepair.com