Many newer LED TV's operate on DC voltage and have an external 110V AC to 16-19V DC adapter/transformer. It would be simple to find a 12V DC to 16-19V (whatever flavor your TV prefers) laptop power supply and skip the 110V AC altogether. We found an LG 24" LED TV from Best Buy for $159. It was a bit bigger than we expected to get, but the price was right and we had a wall space to hang it.
The DVD is similarly small, but we need to find a DC adapter for it as well so we don't have to run it off the invertor. Small DVD players can be had for $50-60.
Both draw very small amperage, so it would be easy to run off a small invertor. LED TV's and DVD players use nothing near the amount of power as old tube TV's and VCR's...and even Plasma and LCD TV's use more power than LED.
Short answer: Forget counter space--wall hang it!