IDRISI

Idrisi gets used here to rasterize vector layers. Convert from Mapinfo to shape using Global Mapper, or Mapinfo. Then use IDRISI to convert from shape to IDRISI vector format. Then use IDRISI to convert from IDRISI vector to IDRISI raster.

To import/convert in IDRISI:
File>Import>Software-Specific Formats>ESRI formats>SHAPEIDR

To convert between vector and raster:
Reformat>RASTERVECTOR

Note - you might be converting from Mapinfo to shape, which will create multiple geometry types. Make sure you convert all the geometrys. First create an image using Data Entry> INITIAL, create the empty image and then add rasters to it.