If you're doing whole brain correlation and correlating the average from a seed region with the whole brain, you should observe almost perfect correlation between the seed timeseries and the region in the brain from which the seed timeseries was extracted.

Do the correlations make sense based on your groups and hypotheses?

The absence of negative correlations may be due to the absence of a global regressor in the 3dDeconvolve command. There is debate in the literature as to whether it's inclusion is a good idea or not. You should have a look at the following papers. (You should be able to find Ziad's paper in the message at the top of this message board.)

59. Murphy K, Birn RM, Handwerker DA, Jones TB, Bandettini PA. The impact of global signal regression on resting state correlations: are anti-correlated networks introduced? NeuroImage. 2009;44(3):893–905.
60. Saad Z, Gotts S, Murphy K, Chen G. Trouble at Rest: How Correlation Patterns and Group Differences Become Distorted After Global Signal Regression. Brain. 2012.
61. Weissenbacher A, Kasess C, Gerstl F, Lanzenberger R, Moser E, Windischberger C. Correlations and anticorrelations in resting-state functional connectivity MRI: a quantitative comparison of preprocessing strategies. NeuroImage. 2009;47(4):1408–1416.
62. Anderson JS, Druzgal TJ, Lopez-Larson M, Jeong E-K, Desai K, Yurgelun-Todd D. Network anticorrelations, global regression, and phase-shifted soft tissue correction. Human Brain Mapping. 2010;32(6):919–934.
63. Fox MD, Zhang D, Snyder AZ, Raichle ME. The global signal and observed anticorrelated resting state brain networks. J Neurophysiol. 2009;101(6):3270–3283.