In that case you probably have a shutter fault. (Blank film is unexposed film, but if it's black film then report back as the causes will be different). The other possible causes would be that the film has either failed to engage on the take up spool or that the film has engaged but is not being wound on by the take-up spool, this could happen if the rewind lock button has got stuck (but then the rewind crank would not turn when you advance the film and the rewind action would be *very* brief). Another cause is that the mirror fails to flip up during exposure, but then your camera would sound very different and you'd notice that the viewfinder doesn't black out during exposure. As you didn't mention any of these obvious signs, I'll continue with the shutter.
Rewind any film and open the camera back. Remove the lens. Use the film advance lever to set the shutter. Hold the camera up to the light and press the shutter release button. If you don't see any light then it's a faulty shutter. You may wish to repeat the test at all shutter speeds including the B setting. If the shutter proves to be fine, then try again with the lens attached (remember to remove the lens cap, and set the aperture to it's widest setting). If the fault only occurs with the lens attached then it's a lens fault if it only happens with that one lens, and a different fault within the body if it's with all lenses.
If everything proves negative and you find no fault, then check with the last lab you used to see if they have an equipment fault. If the film is totally blank with not even any frame numbers, brand name nor bar codes present then it's been chemically bleached out
The FM2 has an entirely mechanical shutter which is usually highly reliable, and it's a model which I've very rarely encountered any serious faults on. Every fault I've had to deal on them with has been caused by abuse, lack of servicing, or simply where an example has clearly been so heavily used that it has worn out. As the batteries are used for metering only, the battery box and light meter can be ruled out as possible causes leaving you with a purely mechanical fault.
This is good as it means your FM2 is very likely to be repairable, but it's not a DIY repair. If your example has had a very long and hard life and is looking very battered, then let it finally rest in pieces(!), but otherwise I suggest that you book your camera in for a CLA service (Clean, Lubricate, Adjust).
Your FM2 will be anywhere between nine and twenty eight years old, so if you're lucky the fault is just due to dried out gummed up lubricants. If you're unlucky then many parts are still available new from Nikon and there are millions of them in circulation so used parts are widely available. Any experienced camera repair technician will be very familiar with the FM2. I'd strongly suggest that you take the chance to get the foam light seals and mirror buffer replaced at the same time as if they haven't already turned into a corrosive black goo then they soon will; it's a one-off job and modern materials will last the lifetime of the camera.
You need to be aware that you're looking at spending a minimum of £80-£90 for repairs (more if parts must be replaced) and this exceeds the price of a used FM2. But even if you buy a used example, it's still going to need the CLA and seals unless there is reliable proof that it has been done recently by a professional technician. For what you may need to invest there is simply nothing else which comes anywhere close to the build quality of an FM2 and once serviced it should be good for many more years of use (although I'd recommend a CLA every few years).
A fully serviced FM2 in good condition is one of the few 35mm SLR's which is still in great demand, and so will be worth around £180 if sold privately. At that price, most repairs will be economically viable.
If you're in the UK then I can highly recommend A J Johnston
for Nikon repairs, current turnaround time for most FM2 issues is about ten days.
I hope that my reply has been of assistance, if so then please take a moment to rate my answer.