Your hands are dirty!!!! Well, gloves. I have the same gloves :P
Seriously, for the tap. Try WD40 or similar product. "Penetrating Oil" is what you're looking for. Leave the tap over night with plenty on the joints and pivots etc. In the morning, with luck, you might be able to turn it.
Another methods to try (either before or after the WD40 method) is to get some Pipe Freezer. This stuff is used by plumbers to freeze a section of pipe, so they can cut it out, without worrying about turning off the mains. Yuo can either use this to carry out the work in the house, or spray it on the joint. In much the same way that heating a nut and bolt works, so does freezing it. I assure you it won't cause any damage.
You might however (cause some, or recieve some when you slip and cut your knuckles).
Hope this helps. If not post again (or PM me - just fancy that, a PM from a Dev!!!!! I'd never close my PM box again...).