I'm with Allen (Airfrogusmc) in thinking you have a problematical transmitter.
You should have got a PC sync cord with the studio strobes, and your 40D has a PC socket, so I would first test the strobes by using the cable for sync. If you get a good result from that you will know that your issue is with the radio trigger system. Based on some of your comments I think it is the Tx that is the issue, but I would still try this to check anyway. Then if you get issues in the future you know you have a backup system. I use a cheap unbranded Chinese RF trigger, and in one industrial location there is a lot of interference from machinery, which triggers the flashes, so I use the PC cord in that location.
When you say you used the test button, was that on the Tx? If it was then it seems as if the TX is able to send the radio signal correctly to fire the strobe. In that case my next move would be to take a small length of wire, an unfolded metal paper clip will do, and use it to connect the pin in the center of the Tx hotshoe foot with the contact in the groove at the side of the foot. This should trigger the flash, since all the camera does is make this switch at the correct point during the exposure when the shutter curtains are fully open. If this works, and other flashes work in the hotshoe, then it would seem as if you have a problem with the alignment of the contact pins, either it goes not far enough on to the hotshoe, so the contact doesn't make, or you have gone on too far, and the contact is past where it should be.