I cannot tell whether D1 (the one that we don't pretend is D2) is connected to R1 (which I decided to call the one marked R2, since there's only one resistor), since you don't use junction "dots", but if they're supposed to be joined, you are short circuiting the motor (+ the leftmost D1).
If they're not joined... To run the motor, the NPN needs to open and for this to happen, the PNP should go open.
The PNP won't open until it's base is ~0.7V less than the positive side of C1, but since the cap will be loaded down by the solar panel when there's not enough light, the base will never get below the emitter, except from the effect of the LED, which will keep it open when the voltage on the cap is reaching U_LED + U_eb (around 2.5V to 2.6V with a red LED).
Since the base of the NPN isn't kept in check, it might get very leaky, draining some of the current produced by the solar panel when the PNP is closed. A resistor between base and emitter (10k to 1M will get it in check.
A solar panel with data stating 6.5V and 40mA is not 6.5V@40mA.
The unloaded voltage is 6.5V (@0mA) and the short circuit current is 40mA (@~0V). This is at a light intensity roughly equal to full sun at noon in the summer.
The electron hole (or is it a quantum well) at the top of your schematic may influence results.
You know, Wilf has spend quite a bit of time with BEAMs, so I think it's safe to say that he would have made a similar circuit if it would do anything even remotely usefull. There's a plethora of Solar Engines out there and you could do worse than using a circuit unmodified.
If you just want a solar power supply to run the motor whenever there's enough light, pick a motor and a solar panel that will work in that setup and just use the panel, a (Schottky?) diode and a motor. It won't behave very BEAM-like though.