2001 Chevy S-10 Blower Motor

You say you replaced the relay. Did you check the relay socket for power? The system runs the lower speeds through the resistor pack. High speed is a direct feed from the relay bypassing the resistor block.
Check the HVAC 30 amp fuse in the block under the hood.
Do you hear the relay switch when you select high?

The relay gets it's on/off power through a different feed. The blower high fuse is a different fuse under the hood. From what you are describing the problem almost has to be the fuse or the fuse socket or the orange wire which takes the direct battery feed over to the blower relay.

Use a meter and see if you have 12 volts on pin 87 of the relay socket with it on high. I would bet you don't. The way high works is that you select HIGH, this turns on the relay which sends 12 volts from the 30 amp fuse through the orange wire to pin 87, through the relay contact to pin 30 and through the purple wire to the blower.
With the relay out of the socket and the blower switch on high you should find TWO contacts that have 12 volts to them. Those are #86 and #87. 86 is the relay trigger voltage, 87 is the main feed from the fuse.

If the blower is working at other speeds it is OK, the only parts on the high side are the switch, the relay and the wires. Since you hear the relay it isn't the switch. That leaves the fuse and the wires. Since the blower does work on other speeds the purple wire from the socket to the blower is OK.