What would it cost to fix this problem?

The F4 E1 is a code that signifies a WASH MOTOR issue.

This is usually caused by: A loose connection in Wash Motor Circuit, Motor Communication Circuit and/or an open wash motor. 1. Unplug dishwasher or disconnect power. 2. Check all connections in Wash/Rinse Circuit and Motor Communications Circuit with meter. Fix/replace an open connection/part. Motor fuse on control open. 1. Start Service Diagnostics Cycle using keypad and advance through the error code intervals to interval 19. ( shown on image below ) 2. Listen for 2 relay contact clicks at the start of interval 19 (to confirm both the pilot and motor relays are turning on.

NOTE:
These relays provide power to the motor, but the motor does not start until it receives a start command later in the cycle). If hear only 1 or zero clicks and wash motor does not come on later in service cycle, and there were no loose wire communication wire connection when checked above, then unplug dishwasher or disconnect power and replace control.

Faulty wash motor. 1. Unplug dishwasher or disconnect power. 2. Use inspection mirror to inspect for water leakage and/or overheating on the wash motor. If evidence of overheating exists, replace wash motor. If evidence of moisture exists, check seals and hoses.

Cost depends on what is needed and how much labor. Check to see how much a new one costs vs. repairs