I don't know if this has been resolved, but here's why it won't work. If a motor is rated at 4 amps, that is its rated RUNNING current. Electric motors can draw 5 to 8 times its running current when starting, so your motor would be drawing anything from 20 to 32 amps. Your power supply is most likely an electronic transformer, the regulator won't allow more than its rated current to flow.
The unloaded transformer will show over 13 volts unloaded. That's normal. As the load (current draw) increases, the terminal voltage drops. If you're exceeding your transformers output current rating by 2 to 3 times, the terminal voltage at that moment would be significantly lower than 12 volts.
A car battery can handle a MUCH higher current draw before dropping its bundle. Much, much, much, much, much higher.
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