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I see two possibilities. The first (least likely) is that the protection diode between the 300 Ohm res and the SLAB is leaking. The second (and the only plausible) source of voltage is the PV panel. Even in complete darkness the panel will be acting as an antenna for local fields, and it's a string of PN junctions (diodes) after all.
You haven't told us which type of LED, but a standard 5mm red LED will turn on at about 1.8V and many will illuminate at 2 or 3 mA (not at full brightness, of course), easily achievable from a PV panel in a moderately noisy area. Short out the PV panel when it's in darkness - if the LED goes out I claim my prize.