What makes you think it's not firing? Rough idle, poor mileage, a black spark plug? Chances are it's firing but making the same power as the other three. A miss is pretty easy to find....pull the plug wire while engine is idling and if the idle doesn't change, the cylinder is missing. If it does change, it's firing/not missing and you move on. If you're getting a jerking or somesuch at speed/moving, that's another issue too.

One of the major portions of a ring job is removing the engine....on my Saab it went $800 plus the engine rebuild....even on a volvo 7xx I still remove the engine and the trans as an assembly...somewhat easier than on a front wheel drive, but still expensive.
It can be done in the car but I wouldn't recommend it, harder on the back. As for rebuilding the engine, what year is the car, how many miles, etc., but in general a 10year old car isn't worth rebuilding the engine (although I did have the engine/trans rebuilt on my 87 Saab four years ago because I simply like the car and didn't want to spend $4K on a nused car and have someone else's problems, you may feel the same). I would check mightily for a factory rebuilt from Volvo or even a new engine or a low mileage later model model engine (if it has a diffo ignition/injection system just use your manifolds/distributor). I'd guesstimate about $3500 today for a straight used engine swap so look around for a volvo rebuild.