If your Hoover steam cleaner can't get it done and you've used it repeatedly, you'll have to do what Steve mentioned and that is a full restoration, to include carpet dye if the carpet is old. The wall outlet cleaners will do a good job IF you go very slow, pretreat the carpet with cleaner, and then rinse it out with plain water, and dry stroke it to remove as much water as possible (that's where the wicking comes from - the pad gets wet with dirty water and as the carpet dries up top, the dirty water wicks to the top), but if the carpet is trashed and loaded with soap, you need horsepower, a carpet scrubber, and a skilled tech to fix it.
Chem dry is worthless; it moves the dirt around but doesn't have the capability or power of rinsing and sucking the dirt out. What a pro will do is pretreat the carpet with emulsifier and then use a rotary buffer/scrubber to scrub the dirt out of the carpet fibers, and then use hot water extraction to suck it all out.