Fuses are almost always clear glass so you can see if the element is OK or burnt out, but I've seen a few like this. I don't know what the thinking behind this is. Sometimes something like this isn't so much of a fuse as an direct electrical connection. Hard to tell.
If you have a multimeter, pull the fuse and check the resistance across both ends. If there is continuity it's OK. If there is no continuity, the fuse is bad.
If you don't have a multimeter, just pull it and take to Radio Shack, or somewhere similar and get a new identical one (you might have to buy them in a five pack). It shouldn't cost that much, at least it should be cheaper than a new monitor.
