Clipping raster using vector polygon in ArcGIS Desktop without having Spatial Analyst?

I have ArcView 10 and I'm trying to clip a DEM (TIFF) to a wilderness boundary (polygon). I know ArcView won't let me do this without Spatial Analyst which I do not have.

I tried exporting my raster and vector in QGIS but I can't get the two to line up (different coord systems).

I've tried to "DEFINE COORD SYSTEM" in ArcToolbox, but something just isn't right.