No solar panel, and for the reason you stated - it is so far from the Sun that a solar panel would be of little use (and a lot of extra weight) at the distances where the primary part of the mission was being performed. The power source is called an RTG. We can think of it as similar to a nuclear-powered battery or a miniature nuclear power plant. As far as I know it is not intended to reach any other star. If it does, it's power will have long since depleted - and it would take thousands of years at its current speed to reach even the closest star. Closest star: Proxima Centauri, slightly more than 4 light years away. Current speed of New Horizons relative to the Sun: 4.52 km/s That's 0.000048 of the speed of light. It would take more than 20,000 years to reach Proxima Centauri *if* it were heading in that direction (which it is not).
It uses the nuclear decay of plutonium in a 'Radioisotope Thermoelectric Generator, or RTG. The heat of plutonium decay is captured and converted to electricity. Pioneers 0 and , Curiosity on Mars, and other deep-space probes use this, as the sun's light is too dim to use solar panels.
