Ditto Roskoe.

I would suspect that your trigger has been adjusted excessively causing the trigger to not engage the sear when you flip the safety off and also causing the trigger and sear not to engage when you close the bolt.

The safety on a Remington seaperates the sear from the trigger when it is engaged. If the trigger is excessively adjusted to remove the take up (creep) the trigger and sear will not engage each other when you close the bolt nor when you flip off the safety thus not having anything happen when you close the bolt on fire and firing when you flip off the safety after closing the bolt with it engaged.