Scheffe is incredibly conservative and inappropriate for pairwise
comparisons (it corrects for all linear contrasts).
Even if a less conservative procedure is chosen there is no guarantee
that any pairwise comparisons will be significant. Significant omnibus
F merely implies that there is at least one significant linear
contrast. It does not guarantee it is an interesting one. This is one
reason why planned contrasts are superior to omnibus testing and post
hocs.
For good all pairs power in this case (with significant omnibus test)
you might consider the procedure suggested by Dayton (1998
Psychological Methods I think) - to use AIC to select the best fitting
pattern of differences between the means. This will be more powerful
that the standard post hoc procedures by some way).
Thom