I recently bought an FG at a garage sale. It was "broken"... it needed batteries - but before I diagnosed that problem, I was a tad baffled by its behaviour (until I figured out how it worked). It only released the shutter at M90, and of course the meter was blank (LCD type). I put in a set of batteries, and nothing happened - I actually referred to it as a paper weight... until I decided to just check things over one more time... and it turns out that in all my wisdom I put the batteries in backwards.
So do check that - its a lot easier to do than one would think.
As far as your camera goes, it is basically acting as if it is not getting any "juice" - right? Or does the shutter release and mirror return at speeds other than M90? In a no power scenario, the sutter will only travel one way and the mirror will stay "locked up" (dark view finder) on all settings but M90. If the batteries are good and in properly... well, it may be a matter as simple as battery terminals. Check for oxidation - a little will be enough to put sufficient impedence to prevent the batteries from doing their job. The next step, if that is not the case, is to investigate any soldered connections - I don't know how handy you are, but that is something best left to a pro, or at least attempted with a repair manual in hand. After that - I am at a loss. The only other thing I can think of is that my FG would get stuck, the meter would light up, but would not move with the apperture ring movement. I found that pressing the battery check button would get rid of the problem, and it has stopped occuring all together - I assume there was some literal or figurative "rust" in there somewhere which went away with regular use.
Do make sure that you have a strong light source, as indoor conditions are tricky - we sometimes do not realize exactly how "dark " it is around us. Go outside or point the camera at a lightbulb. Start with slower speeds and higher ASA, just to make sure youare within exposure range. You mention themeter "hovers" around the low numbers - which is its "at rest" position - high or low? If it rest at the high speeds, you simply need more light - as the meter demonstrates that it travels through its range to arrive at the low values (that is the set up on most cameras I've seen). If its down there because that is where it rests... then we're back to square one.
I would be a bit worried if the shutter fired at all speeds, but the meter didn't meter... that could be more complex, and frankly, probably worth more than an FG20 in monetary terms...
Also, here is a page that I found very useful (there is an FG portion as you will see, the link is for your FG20):


Hope you figure it out - it is a nice little camera when working properly. Nothing fancy, but very compact, light and handy, and (this is coming from a Canon guy...) takes all that great Nikon glass. Even the E-series 50mm on mine, while a bit sloppy construction wise, is sharp as a tack and gives great contrast and colours. And, after all, it is the glass that counts