3.7v DC motors not drawing enough current

The 1N4148 diodes are definitely not appropriate for those motors as the maximum repetitive forward current is only 500 mA. They may already be damaged. Try 1N4004 or similar.

Also, breadboards are not intended for high current (> 100 mA or so) and the contacts may be burned, especially the power rail. Solder all the motor connections.