As Andreas has pointed out, given the age of the camera there is a good chance the capricious capacitor caved.
You can test this as Andreas mentioned -- once you get the film out. Make sure the camera is OFF, with a good battery installed. Set the camera shutter dial to "A". Turn the camera on. While looking through the viewfinder, press the shutter release slightly to see if any LED lights up. Press it all the way, and see if it goes out. If it does, the capacitor is the problem. If the shutter fires, no problem.
Capacitors are cheap and you can replace it yourself if you have the tools, materials, the time, and some soldering experience. A repair shop can do it, but it will probably cost more than a working body. FYI, the X-300 was also sold under several other names. See --
http://www.subclub.org/minman/x370.htm