W/O knowing what's between your roof and the ceiling in your attic, the solutions will vary.
Of course, if you know what's there, then a little research will tell you if demolition and re-doing the job right is the way to go. Although you have a ridge vent, one can't be sure if soffit chutes are in place. However, again, some research will help you find out. If you can tell that there are soffit chutes between the rafters, then all you may need to do is have soffit vents put in. Depending on your construction will dictate the material for the soffit job. Assuming you don't have soffit chutes and the roof is actually fully insulated, you may be in big trouble. In short, the life of a roof is extremely shortened in this situation. The shingles and the sheathing will deteriorate faster than you'd like. This is a worst-case scenario. In this case, in my opinion, the best thing to do is the right thing to do, and that's to properly vent the roof. This means demolition and re-finishing the inside. Not what you want to hear but the proper solution.
So, if your poking around the roof reveals that you have chutes under the sheathing, then I'd simply put in soffits and see what happens. If you're in the worst-case scenario, you can try some Heat Tape first. The major home centers carry it. This is not a cure-all so don't be mis-led! In fact, I'd only recommend it if you get SLIGHT damming low on the roof eaves. (If you only have to put in vents, and next year you get a little damming, try the tape next. But you electric bill will go way up!) If your damming is more than a foot or so up the roof, it's a waste of time and $$$ (you have to pay the electric company too forever. Not cheap).
You can search the web for keywords such as ice dam and prevent using your favorite WEB Search Engine, and you'll find lots of hits on the subject. I've included a few sites for you to read. One site is from U-MASS's Building Materials and Technology, one is from a guy's personal experience where he let the problem go too far, and the 3rd goes into the Heat Tape option a bit more with contacts for you if you can't find it. The key is to find the cause to determine which solution is the best one. My best to ya and hope this helps.