Rick at Audio Alternative in Fort Collins Colorado is probably one of the best Linn guys in the country.
If you are willing to ship I recommend audioalternative.com, they are in fort collins colorado but well worth the time and shipping expense. As far as I have never seen Rick is the best on LP12's from stem to stern and will fix any problems you may have. I bought mine from him and he has kept it in perfect condition and it was used when I got it, and I would compare it to any brand new ones. If you don't have a box he will ship you a box with instructions on how to pack it. Most definitely worth a call.
Mofi and Theo are right. It is not hard to do yourself. I rebuilt two LP 12's after watching it done, and did it without a jig. Just take pictures of the bottom and load them into your computer so you can screw the wires in, in proper order. Hopefully the motor is not gone. That's a little harder. I have pictures if you need them. Best of luck.
I realize you are on the East Coast, and you've already got a few members (Mofimadness and Theo) who have given you a source in Fort Collins Colorado, but here's my 2 cents worth. I live out in California....(yes I know it's further away from you than Colorado, but if you're gonna ship your 'table anyway?)...There's a groovy little Highend Audio store in the Los Angeles area called "Shelleys Stereo" and they've been around for many, many years and are great guys. They have an old fellow named Stan who is quite the Linn guru. He has done work, and rebuilt my LP12 from the ground up. Very meticulous and detail oriented, knows his stuff, and a super nice guy. I too had the same issue with my Valhalla (internal) power supply which he rebuilt for under $100.00, and now workes flawlessly. I'm like you...technically "challenged" and not comfortable playing around with electronics or repairing them. Stan does great work. You can Google "Shelleys Stereos" in Woodland Hills, California. Great experiences for me dealing with Stan and the guys there. Just thought I'de add to the other suggestions and resources given in this thread. Good Luck.
Jcbach. Call David or Alma Wilson of accenthifi in Mt. Kisco, Ny 914-242-0747 they are very good to deal with and but from. You might as well check with others for hourly rates. Linn is usually 95.00 per hour. That way you can ship the unit to the closest to you or the best on labor. If you try it yourself, unplug the unit first, its live even with the power switch off. Good luck.