The Ricoh FF-3AF is a compact autofocus camera released in 1982. Your model could be over 30 years old!

The shutter release is electronically controlled. Your problem is going to lie in one of two places:

• The shutter release button is stuck. The release appears to be completed by closing a circuit. Perhaps the button itself is stuck such that, when the top is on the camera, it is pushing down. Test this by attempting to load a role with the top off and the shutter release mechanism clearly disengaged.
• If the problem persists, the electronics have gone. Either a problem with the button mechanism itself or somewhere else in the circuity. If this is the case, the camera is junk (yes, an electrical engineer may have a go at a repair - the rest of us mere mortals will simply toss the camera)

I accidentally bumped a piece and now it's jammed somewhere inside.

First rule of any repair: don't make the problem worse in the course of your repair. ;-)

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With older gear, the cost of repair is generally much, much higher than replacement value. As of this answer, pristine condition FF-3AF's on eBay are going for ~$20 to $30. Having a repairman even look at the camera for an hour will probably cost more than that.

Your best bet with any old autofocus compact is to use it until it dies and then replace it.