It seems likely that your F-lock key has gone bad. The fix requires disassembling the keyboard.
I've had three or four MS Natural Ergonomic 4000s, on each of them a different key failed. On the single one that I bothered to troubleshoot the two plastic sheets which compose the "switch" part had slid out of place slightly. Unlike most rubber-dome keyboards, which have a single plastic sheet with a wave-like pattern for the carbon pad to press, the MS 4000s have two sheets which lie one above the other.
In short, your keyboard needs either replacement or repair. If you cannot repair it yourself, then replacement would likely be the less expensive option.