Wipers work only on fast

I have a 2005 Grand Prix. The wipers only work on fast speed and when I shut them off they stop in the position they are in. This happened a couple of months ago for a day then started working again. I managed to get them to work regular for a brief time (seconds) by playing with the wiper switch. Might it be a relay going bad or is it in the switch itself. It doesn't seem to be mechanical.

Are you saying they "park" in the up position all the time or they sometimes park in the normal position...

HI works, but low doesn't? Does pulse work?

don't have an idea to that ..

Just as an info, as I do not have the specific experience on that model, but on former GM years, solder around the plug contacts on the wiper module used to break and that lead to totally erratic wiper behaviour. If nothing else comes as the solution, maybe it could apply too.....
http://www.automotiveforums.com/vbulletin/showthread.php?t=677547
...and in fact, this is a no risk 0$ fix that can be tested anyway if such module exists in this mdel (well maybe it is part of the body control module now...????)

However in the case of my son's former Lumina Z34 , the motor mechanical unit was at fault...NO problem with his GP2000 yet..(on that matter...).

..edit:..as yu suggest indeed I read there are 2 relays in this model set-up....

Thanks for the suggestions. Now I just need to get under the hood.