The firing pin problem was that the pin would break and the broken piece would jam in such a way as to cause it to go full auto. There is a good chance that yours is broken and the piece has already fallen out. Yes, you'll need to strip it down and get at the firing pin to determine if it is in fact broken.
Winchester (I'm talking about the corporation formerly known as Winchester) would send you a new firing pin and actually pay a small amount to have someone put it in. I don't know if the new corporation is taking responsibilty for fixing them or providing new pins.
First step is to get it stripped down to determine what the real problem is.