I would work out the heated bed issue first. It's probably either shorted to ground or you have blown the FET that controls it.
If the extruder motor runs fine on the X axis driver then it's not the motor or the wiring. It's either a blown extruder driver or a wrong current setting on the driver. A DVM will tell you quickly where the current is set on the two drivers. If they are plugins you can move them to see if the problem follows the chip. If they are plug in's there's a sight chance that it's a bad solder joint on the board they plug into.
If the extruder motor runs fine on the X axis driver then it's not the motor or the wiring. It's either a blown extruder driver or a wrong current setting on the driver. A DVM will tell you quickly where the current is set on the two drivers. If they are plugins you can move them to see if the problem follows the chip. If they are plug in's there's a sight chance that it's a bad solder joint on the board they plug into.