When you connect the LED ground and see the ADC sampling problem, what sketch is running on the Arduino? It could be that turning on the LED is affecting the power supply and hence disturbing the ADC. Try connecting your scope to Vcc. Also check Aref (the ADC's full-scale reference voltage) and AVcc (connected to Vcc on Unos, but may be different on other boards).
Another possibility is a software bug: is there any chance that you write to the ADC pin by accident? Try replacing the preamp with a simple voltage divider (providing 2.5V). Then modify your code to generate a stream of LED pulses and look for glitches on the ADC input.
BTW, when using a transistor as a switch the "common-emitter" arrangement often works better. The "on" voltage across the load is higher and depends less on the load resistance. Eg.