Kimmy, you might want to have your local bike store (LBS) do a thorough cleaning of your DRIVE CHAIN/GEARS area. Tell them to remove your chain and degrease it thoroughly and also remove and clean the cassette and the clean the front gear rings and the derailleur wheels, etc. YOu can handle the rest of the bike. If your chain has that much hardened gunk as you describe I can't imagine getting it totally clean without taking it off.
The other thing is that if you've been running your chain really dirty and gritty for a long time, it may be worn enough to have them put on a NEW chain when they clean your gears. Chains don't last forever. Then you could start from ZERO dirt!