Is there no way to run DC motor at very slow speed only using Arduino's built in power supply?
Not using the onboard 5V regulator but it is feasible to have a uController programmable power supply that takes a command from the arduino and outputs a specific voltage. Using an LM317 adjustable regulator and either digital pots or analog switches and resistors that can be switched in parallel to change the adjust voltage that is normally done with a 3k to 5K potentiometer. I have the analog switches (ADG511BR) and the surface mount to DIP adaptor and resistors to do this. If I went to Fry's and bought the LM317 adjustable regulator I could have a programmable power supply by lunchtime. Switching resistors in parallel with each other lowers the total resistance. The analog switches are designed to be controlled with a TTL 5V Logic signal so the design is extremely simple and guaranteed to work every time. It's not any kind of exotic circuit so any Newbie could implement it if they could solder the surface mount chips onto the DIP carrier. That would probably be the only show stopper for some people because the pins are very close to each other. If you can find an anolog switch in a DIP package then you could do it. It seems they don't make DIPs any more but China has a ton of old surplus chips they bought from the us during the past 20 years and are not selling back to us on ebay one by one. (a 5 cent 14 pin chip sells for $2. go figure)