Multimeter cannot read below 200ma
It is almost certain that you have a blown fuse on the 200 mA range.
This is extremely easy to do and it is common to find meters wity this fuse blown.

Open the meter. There is almost only this one fuse.
Replace it with one with the same current rating. 

If you want to live when you plug the meter into AC mains when it is set to the 200 mA range (as happens) then use an HRC (High rupture capacity) fuse. These usually have a ceramic body. An HRC fuse is rated at say 200 mA (which typically has about a400 mA fast blow rating) fusing current PLUS the ability to break an arc when currents of hundreds of amps start to flow. Residential AC mains is usually capable of supplying a fault current of hundreds of amps. If you plug a fused 200 mA meter circuit into AC mains the very large fault current will blow the fuse in under a milliscond - but an arc may well form across the fuse. An HRC fuse is designed to not support an arc up to current values of hindreds or even thousand of amp. A non-HRC-rated fuse will often allow an arc to form and maintain. Death can happen.