Connect your replacement switches back-to-back with a fiber patch cable and verify for sure that their fiber ports work. If they do, then double check the patch cords you're using at each end in the same manner. If you really want to slog through it yourself and have the right patch cables you can use the switches as cheap testers to test at each of the splices (assuming you have connectors on the splices).
If the switches do work, get a better fiber contractor in there. It sounds like your contractor was dodgy. I agree w/ the other posters re: their meter. My experience with contractors testing fibers for me is that their meter knows far, far more than I do about a given fiber.
The TFC-1000MSC has SC (square) connectors, so if you're using ST (round) termination, you must be using some sort of dongle or coupler between the ST jack on the patch panel and the SC fiber jack on the fiber converter, right? Is the 3-meter test fiber terminated SC-SC, or are you using an SC-ST dongle or coupler for your test? Are your old 100base-FX fiber converters SC or ST?
In general, fiber is fiber. We use both 62.5/125 and 50/125 for 1000base-SX connections have no problems with either (using LC or SC termination). However, this page notes that if you have to couple multiple fibers together, it's important that all of them be of the same type, or you can get light loss.
If you're using all 62.5/125, then it may be that your ST connectors are not designed to pass the wavelength of light used by 1000base-SX. If you look at the Wikipedia pages you referenced, you'll see that 100base-FX operates at a wavelegth of 1300nm, while 1000base-SX typically uses 850nm. I don't know if connectors even have such limitations or not, but I do know that ST is not commonly used anymore, and I've never seen it used for GigE.
Also, keep in mind that 100base-FX and 1000base-SX are not compatible. If you're only testing one end of a run at a time, you definitely will not get a link. Aside from the fact that the use different wavelengths, neither of them is 10/100 or 10/100/1000 auto-sensing. In my experience, this is not universally understood. :)
Best Answer
No, not by design, though it wouldn't be hard to design a NIC/module that could handle both but you'd need to let us know what equipment is at the gig end to allow us to help you on that.