When the pump is running the water is going to always take the path of least resistance, so if your steam wand is leaking then all the pressure will be redirected there and there won't be enough to open the brew valve. Pushing the coffee button simply turns the pump on, and if your wand is leaking this has the same effect as turning the steam knob and engaging it's pump switch.
If you've already tightened the knob as much as possible and the wand is still leaking, it's possible the valve seal is damaged or missing. You'll need to remove the steam knob and shaft assembly and then inspect the valve seal; it is a small white teflon washer, part #9 on the second page of this diagram:
[http://partsguru.com/user/Barista%2005.01.pdf]
If the washer has a deep groove worn in it, try flipping it over as this may buy you a few more years out of it. If it's broken or missing entirely then the valve will not seal and the wand will continue to leak until it's replaced.