It sounds like scale to me.... I've never messed with a barista.... Might need a deep de-scale.
Do you get plenty of water out of the shower head without the portafilter installed?
Could be the pump. On does not always mean good.Disconnect the pump from the boiler and see if water is flowing.
And water does not flow out of the steam wand?
Have you checked to see if the water is going anywhere else? The drip tray or leaking inside the machine. I'm not familiar with this machine, does it have a pressure relief?
Here's the parts list for the Baristahttp://espressocare.com/Qstore/Qstore.cgi?CMD=009&DEPT=1158362623&CAT=1158972009&SUBCAT=1158974604&ADMIN=YESHave you been descaling it regularly?I'd pull out the brew valve (42-45) and take a look at it. It is probably similar to the Gaggias without 3-way solenoids, and tends to get clogged with scale. A straightened paperclip can be your best friend.Susan