I had this issue with my 50D. I did the isopropyl trick (google it) and it has worked. Eventually the issue resurfaces, but another treatment of the isopropyl trick and it's fine for a while. I do not have the funds to replace the shutter button at this current moment.
A new shutter button is ~$15 IIRC from Ebay...if you have any electronic background, have some ESD equipment(atleast an ESD work mat and wrist strap) you could replace it for free(or for just the cost of the part!)
If not, there are many people who will fix it for you...me included..
Just saying, there ARE other options than the ~$200-250 fee from Canon..or just dripping alcohol into the shutter button in the hopes it will clean the contacts and "fix"(temporarily, or if at all)...not saying this isnt a good thing to try...or that it doesnt work. Just saying I would fix it properly because it would only cost me ~$15...
BTW, to the OP..
I dont think the shutter button is your issue...it sounds to me like the safety switch function or other user error(it happens! ), but if not, the shutter button is easily the next possible cause..