The arduino digital I/O pins can provide 40mA max and to ensure that your arduino has a long life, it's recommended that you not exceed half of that.
It sounds as though your solenoid needs more power - you'll need to use your transistor to switch the 5V supply directly rather than trying to run it off one of the pins.
It's possible too that you've already damaged the pin you were trying to use - might be worth testing it with an LED and suitable resistor.
I did notice something, though: when I connect the solenoid directly to the +5V power source and the ground of the Arduino, the solenoid moves "to the other end" in an instant.
The playground has a circuit for solenoids: http://playground.arduino.cc/uploads/Learning/solenoid_driver.pdf. Don't forget the diode.QuoteI did notice something, though: when I connect the solenoid directly to the +5V power source and the ground of the Arduino, the solenoid moves "to the other end" in an instant. That's expected behavior.
However, it still only does something when turning the power on and off, i.e., plugging in and removing the USB cable; changing the signal to the base from HIGH to LOW, or vice versa, does nothing, though.What does this mean?
It means you should post a schematic (or drawing) so we can see how you have things hooked up.
Do you have a link to the solenoid you're using?
This smaller solenoid is designed to work directly with 5V which makes it a great match for embedded projects.