Agree with Dan. Unless the firing pin is always protruding from the bolt face (a broken pin can get wedged into that position) most likely the sear is not holding back the striker. Could be due to a worn/ broken part, or improperly installed part.
This is a good news/ bad news sort of thing.
Good news- parts ARE available.
Bad news- if you do not work on these little Remington actions for a living, they are a BITCH to put the pieces parts in the right order/ position. SERIOUSLY suggest you find a good local smith. Failing that, contact Remington customer service, check about returning it for service at the factory. With a safety issue like that, Remington HAS been known to do work, no charge.