One thing you need to check is if the chambered round is flush or below the barrel face, if it's recessed very much, it may have too much headspace, add in the barrel to frame gap and not pulling the trigger all the way to the rear and you get no fires. Read the Handi Basics 101, pulling the trigger properly on an H&R is important.
Firing pin protrusion is measured with the trigger pulled to the rear and the hammer resting against the frame with the transfer bar in the up position. It could also be a bad transfer bar which you can replace if you buy the part from Brownell's, H&R won't sell it, but they will fix it for free if you send it in. If you find the chambered round is flush with the chamber face, you can remove a little from the face of the hammer where it stops against the frame to increase pin protrusion, but that won't fix a bad transfer bar, neither will a new hammer spring. If you end up wanting to send it back, contact them, explain the problem and ask for them to cover return shipping, (toll free (866)776-9292.
Brownell's doesn't sell Wolff springs, they sell the factory spring, Wolff and Midway are the only sources I'm aware of that sells the hammer spring, there is no spring "kit" that I'm aware of, you'll want the single coil.
Tim
http://www.midwayusa.com/viewproduct/?productnumber=565785http://www.gunsprings.com/index.cfm?page=items&cID=2&mID=27