DIAGNOSIS The thermal fuse (also called a thermal cutoff) has blown. It's a safety device that trips if things get too hot, and the intense heat of a self-clean can sometimes do it, especially if the vent path was blocked.
FIX You need to replace the thermal fuse. Unplug the range. It's located in the vent assembly at the top-rear of the oven cavity. You'll likely need to remove the oven back panel and possibly the top to access it. The part number is commonly DG94-00608A. It's a small, rectangular ceramic part with two wires. Swap it out.
IF THAT DIDN'T WORK If a new fuse blows immediately or the oven is still dead, the main control board could have been damaged by the same overheat event.
HEADS UP This is a critical safety part. Don't just bypass it by connecting the wires. You risk a fire. Make sure the oven cavity and vents are completely clean before running another self-clean cycle.