Where is the valve in my handpump - and what stopped it working? I have quite an old handpump that fits on my frame.

It looks like it's called TOPEAK  "miniDUALG - optimised for MTB/ROAD."

It has a pressure guage and various bits that screw the handle to the body and the body to the end with the pressure/bar valve, with an interchangeable head that allows you to switch between Schrader and Presta / Woods/Dunlop valves.

Last night, when I got a puncture, it wasn't working. The pump was placing as much resistance to pumping in as pulling out (I may even have been drawing air back out of the tyre, I can't remember).  Somewhere, there must be a blockage which is stopping the one-way valve from working.

But where is the air intake for the pump anyway?  In the head (part of the valve adaptor), the middle (it has two sets of o-rings, with some cleverly designed stuff between them), or the handle (which has gaps in the screw thread down which air might flow from the outside — if that cup-shaped head seal would let it).

Anyone got any suggestions?  I'm baffled - but I don't want to throw away a perfectly good bike pump if I can repair it.
If I understand correctly you're feeling the same pressure on the compression stroke as the extension stroke?

The mini dual g pumps air during both compression and extension strokes so this would be normal behaviour https://www.topeak.com/global/en/products/pumps/239-mini