I am having a similar problem with the exact same data types (I am also using Nico's Tobler-derived vertical factor tables, and conferred with him personally on it; I am sure the tables are not the issue).
To be clear, here is exactly how I ran it using the Path distance tool:
Spatial Analyst Tools > Distance > Path Distance...
a. Input: Sites (my source point data--one point selected)
b. Output: aniso_hrs1
c. Input cost raster (optional):<blank>
d. Input surface: colca_clip (my clipped 30m DEM)
e. Maximum distance (optional):<blank>
f. Output backlink raster (optional): aniso1_bklk
g. Vertical factor parameters (optional): Input Vertical Raster: colca_clip, Vertical factor (optional): Table, using Nico's "Tobler_away.txt"
h. "Environments..."> "Processing Extent..." > Set the Extent to "Same as Display"
The "good" news is that I can get it to run using the above, but ONLY if it is zoomed into a small area. Beyond a certain extent (not a very large one at that), it won't work anymore, even restricting the processing extent to Same as Display. If I use the extent of the DEM as the processing extent, it will just return a Euclidian distance grid, ignoring the DEM.
FYI, the DEM must be 32 bit floating point, with square pixels for it to work. That might be your problem. Mine, however, has to do with the extent.
Please ESRI people, throw us a bone.