You are asking whether a photon can excerpt pressure on matter it interacts with.
When a photon interacts with an atom, three things can happen:
elastic scattering, the photon keeps its energy and changes angle
inelastic scattering, the photon gives part of its energy to the atom and changes angle
absorption, the photon gives all its energy to the absorbing atom and electron
The answer is yes, even when a photon hits a mirror (and gets reflected), it can excerpt pressure on the mirror by transferring part of its momentum to the atoms of the mirror.
Now in your case you are asking about a solar panel. Now even if the solar panel was a perfect absorber (it is not), and it was absorbing 100% of the incoming photons, some of the photons' momentum would be transferred to the atoms of the solar panel, thus excerpting pressure on the panel.
Now since the solar panel is not a perfect absorber, all three things happen with it, elastic scattering, inelastic scattering and absorption.
You are mixing two things, energy and momentum. Some of the photons' energy is absorbed by the solar panel, some are reflected. But in all cases, part of the photons' momentum is transferred into the atoms' momentum of the solar panel, thus excerpting pressure on the panel and eventually moving the panel (if it is enough momentum to move it).
The car in your example is too heavy, and there is too much resistance from the road. This will never move the car in a measurable way.
But if you would have your solar panel in space, then yes, the pressure excerpted by the photons that interact with the panel, would give the panel enough momentum and would move the panel. This is how solar sails work.