My hardrive is plugged into my mac, the light is on, the hardrive is spinning, but no icon shows up on my desktop. I've searched my computer, and the icon isn't anywhere. I don't know how to access it even though it seems to be working.

An external storage-device has four major components:

* the USB cable

* the power-adapter

* the disk-drive inside the enclosure

* the USB-to-disk-drive adapter inside the enclosure.

One of these components has failed.

Try a different USB cable.

Try connecting to a different USB port on your computer.

Try connecting to a USB port on a different computer.

Take a "multi-meter" and measure both the voltage and amperage output from the AC adapter, and compare with the specifications on the label on the adapter.

Open the enclosure, and remove the disk-drive, and then connect it as a "slave" disk-drive in a desktop computer, to see if it works at all.

Purchase a new, compatible, disk-drive, and install it in the enclosure, to "revive" your external storage device.

Get the part-number and serial-number from the label on your disk-drive, and access the manufacturer's web-site, and use "check warranty status", to see if they will replace the device, at minimal cost to you.

There exist commercial "data recovery" services that can try to repair your device, just long-enough to rescue and copy your files. For example, see: https://services.seagate.com/index.aspx?lng=en-US for a "no data - no charge" guarantee.