Well, after 7 years of almost daily use, it appears that the pump has failed on my Andreja Premium espresso machine.
The machine uses a 52W, ULKA EAX5 vibe pump – and as it turns out, this is a fairly commonly used pump in espresso machines.  I also found prices varied wildly.  The dealer where I purchased the machine sells the replacement pump for $95.  I found a replacement on Ebay for $39.99.
After getting the new pump swapped in, the machine seemed to be working fine.  Then, this morning, it seemed to have stopped again 🙁
So, removed the casing from the machine and hooked the water supply back up, and this time I tested things out  with the cover off.  This allowed me to see the water flow.  Everything worked fine. Maybe I kinked a hose as I put the machine back together?
I carefully put everything back together – making sure no hoses were kinked, and tested the machine again – everything was 100%.  This morning, the timer kicked in and turned the machine on at 6:00 AM, and at 7:00, I pulled a double shot with no issues.  I think that the shot was up there with some of the best that I’ve done!
Something I came across, that might be useful in future, is this page describing the process of repairing the ULKA pump itself – with lots of photos and additional comments from other readers.  I still have the old pump just in case.  They certainly aren’t that complex!