Ron
the importer of Shop Fox lathes is Woodstock International. Their web site implies that they can supply parts, but I couldn't find where to order them. I found a parts list that identified the circuit board for your lathe as part number DZ-236A1.
For what it's worth, the main distributors of Shop Fox lathes appear to be Wally World, K-Mart, and Amazon. My first lathe was a Shop Fox (model 1704).
But as I mentioned, this looks very much like my Turncrafter, or lathes sold by King-Canada and Axminster - all manufactured in China. Your lathe is rated 12x15", with a 3/4 hP motor. PSI sells a 10" swing version with a 3/4Hp motor, and a 12" version with a 1Hp motor.
Bob of RJBWoodturners has the 10" version, and I believe that he said that he was able to purchase a replacement speed control box for under $90. I don't know this for a fact, but I would guess that the PSI box could be used on your lathe. If you can't get any help from Woodstock International, you might try calling PSI - call technical support and ask for Joe Roberts (he's really knowledgeable).