Are there solar lights that can be put inside existing lamps?
You could maybe buy some cheap solar lamps, and tear them apart to use guts to replace your existing lamps, but my guess is you're going to have trouble mounting the solar panels somewhere that doesn't look goofy. If you mount them away from the lamp itself, then you're going to have to run wiring (and as you said, that was not done well and has been disconnected). If you're willing to run new wiring, then you can definitely use low voltage LED bulbs, where you just need low voltage cable that goes back to a transformer somewhere (or battery + solar panel) - this is much easier and safer to install than high voltage cable (where you pretty much need to run it in a conduit anywhere underground).