I'm guessing you likely have either an LCD or LED TV with 120Hz or 240Hz "motion smoothing feature". This is the terrible, terrible "feature" of LCD and LED TVs that attempt to "fix" the inherent flaw of motion blur on those sets. Plasma sets do not have that problem.
By unplugging and replugging things you certainly activated or set that motion setting. It's called different things on different settings. Disable the feature completely and your TV will return to normal.
Personally, I cannot stand that soap opera effect and it drives me nuts. Check the user manual for the exact setting location. That's what's causing your problem and turning it off will solve it.
I much prefer the slight motion blur inherent with the LCD/LED technology than the terrible fix.