Use the type of lighter fluid for 'Zippo' lighters. It's naptha. Same as what Dry-cleaners use. It'll break the glue down enough so that it will release. Apply it like BHBurban suggested. It evaporates fast, so you can't do the whole thing at once. Small sections about 6" square at a time. Show that carpet no mercy! Throw some muscle into getting it off
Once the carpet is off, put some of the lighter fluid on a rag & lay it over the glue residue left on the panel, and let it sit for a bit. Then once the L-fluid has softened the glue, you can scrape it off with a putty knife. Have patience. You may have to repeat this procedure several times. The L-fluid is cheap. You're gonna be using a fair amount, so pick up a big jug or two small ones.
DO NOT SMOKE while doing this!!! Extinguish all open flame! Work in a well ventilated area.
There is another chemical that you could use, but it's extremely dangerous to your health. It's called 'Xylene' or 'Toluene'. Requires gloves, a chemical mask, & eye protection. It can be absorbed by your skin, & the surface of your eyes. Goes straight to your kidneys & can cause tremendous back pain. Recommend using it in a paint booth.
But it WILL get that carpet off! Hehe!