When I try and use the dissolve tool (vector>geoprocessing tools>dissolve) QGIS 2.16.3 crashes and produces a minidump file. This is with any shapefile that I use. I have also tried it on a friends 2.14.3 and the dissolve process works fine for the same files that I tried.
Try to do clean uninstall of your QGIS software and install it again. To do clean uninstall you can follow the instructions on the question: How to completely uninstall and remove QGIS 2.8.1?. Then install the updated QGIS LTR version of 2.14.7 instead of QGIS 2.16.3, maybe it will solve your problem.
I encountered the same issue a few days ago. A possible workaround is to use the GDAL module (accessible through the processing panel). Both GRASS and SAGA also have tools to dissolve the polygons.
A possible cause for the crash might be linked with the topology of the file, do some of your polygons overlap? I remember an error message linked with that, not sure where though.