Is it a PC or arcade monitor? Well my monitor is a 19" with the same problem. Trust me it is cheaper to buy a new one if it is more than a wire problem! You can get a nice 19" new PC monitor with a 3 years warranty for $190. You are looking to pay atleast that with no real good warrenty in a repair.
www.tcwo.com has some good monitors at nice prices and it is like $8.00 for ground shipping on one.
Now if you have an arcade monitor 19" it is the same deal for the most part you can get a new one with a warranty for under $300 now I am not sure of the shipping cost of it since I just pick that kind of stuff up but I am sure it is a bit more expensive.
Still overall with price drops on smaller 19" arcade\pc monitors it is almost always cheaper or more worth it to buy a new one in the long run!