Drumagog will indeed do this. I saw a demonstrtaion at NAMM where a guy sat in a folding chair with four microphones (SM58s), aimed at his knees and feet. The right foot was generating a kick drum sound, the left a hi-hat. He was tapping his feet on carpet in an extremely noisy exhibition hall! And playing a convincing drum solo in real time. 

I know you said you can't use fingers and have many suggestions from others but I use this little Korg Nanopad and it is awesome. I have the entire drumkit at my fingertips. I also use it for synths, etc and it works great at a decent price.
 
http://www.korg.com/us/products/controllers/nanopad2/
 

Once again, you guys are more helpful than I hoped for! So much here, and I'll go through them carefully!
Thank you, thank you all!

MarioD
If you are going to use your hands then an Akai MPD18 drum pad may help"
http://www.sweetwater.com/store/detail/MPD18/?utm_source=MSN&utm_medium=PPC&utm_campaign=audio&utm_term=akai_mpd18
 
I have one and it does the trick for me, except I use sticks!

These are particularly useful if you buy the pad boosters from MPCstuff.com. Makes them much more linear and sensitive. 
Much of the time, though, I use Step Sequencer. With the ability to 'push' notes in time, add 'swing' and edit all the parameter for every hit, you can make very nice grooves as fast as you can do 3-4 takes. With Addictive Drums you also have more choices from each instrument and many more instruments to get nuance in your snare and cymbals. 
 
I have a drum set, and can hold a groove on a live session (NOT a drummer), but prefer crafting my rhythm tracks rather than pounding them out with my fingers on my upgraded MPD18. 

Another option to try is the step sequencer. You can have it loop 4-8 (or whatever) bars and insert/remove drums as it plays. It also has some nice features with humanizing and adding grace notes (randomness) during looping playback. One other nicety for this is that it is already aligned to your project tempo, so removes the potential variation of "live-to-project" alignment. There is a lot you can do with the MIDI data once recorded, so it can get complex quickly; but as far as a "sandbox for creation," it is a nice tool.