Another great little machine, ahead of its time. May well date back to 1985 or earlier!
... The Mia does not have a self-priming pump,
Sorry to contradict but actually it is a self priming pump, and the priming action you must follow when you have either drained the reservoir or after you have made steam, is quite normal for all domestic boiler machines.
....I then followed the directions for making steam and it seemed to steam quite well, except that when I turned the steam switch off it kept steaming for about 30-40 seconds. Eventually the steam fizzled out.
From memory, the steamer on the Mia is solenoid controlled and if it did not stop steaming alsmot immediately the button was released, this probably means there is some gunk around the slug inside the valve which is slowing the return spring from returning immediately. It may clear of its own accord or someone may have to dismantle & clear or replace.
....Now, I can get water to run through the group to make coffee, but I cant get it to make any more steam. If I follow the directions for making steam I get a few drips of water out of the steam wand. If I keep pressing the steam buttons for about a minute steam starts to come out from near the group but nothing other than a few drips from the steam wand.
As long as the water pump is working, thats good. As long as the water coming from the group is properly hot, thats good (meaning the element is ok). The steaming coming from the group area indicates you are producing steam when deprtessing the steam button, but if it is not *being released out of the steam pipe, then it is simply overpressurising out of the pressure relief valve in the group area.thats good too....but seems like the electrovalve is not re opening.
Sounds like the steam solenoid valve needs attention or replacement... OR, the controlling push button but if there is a probloem with the button, the thing is a four (from memory) *button but SINGLE switchblock so a complete new switchblock would need to be sourced.
Needs service Im afraid.