It sounds like you're getting pretty close to solving your problem.

The 'varnish' I referred to is semi-dried fuel, which turns yellow-orange and very sticky, and no longer smells like gasoline. Normally you might find this in an area where fuel is exposed to the air, like in a fuel bowl or the float chamber of a carburator. You've had most of your fuel system apart and you only found the normal white residue from the metal leaching atoms, so apparently you escaped the dreaded 'varnish' problem!

You still need to determine that you're getting fuel from the gas tank. With a fuel pump mounted as low as these old Volvos' you might be able to just remove the incoming line to the fuel pump and see if gas runs out. That always happens to me when I don't want it to!

I happen to have an electric fuel pump that comes in handy for bypassing the stock fuel pump and it sucks a lot harder than the stock one, too. These are fairly pricey these days, so it's not recommended that you run out and buy one, but if you have one laying around, you might give it a try.

Blowing air back down the fuel line to clear any obstructions is a good tip. I had a 1947 Jeep that had accumulated some rust and debris in the tank, and that junk would manage to plug the fuel pickup fairly often. If you get the car running and find it dies for no particualr reason but restarts after sitting a while, you might suspect that you need to remove and clean out the tank.

Unless your car is showing significant rust on the undercarriage, you probably don't have holes in the fuel line. The metal line is much thicker material that the car body itself.

Have you checked for spark yet? We know you're looking at a fuel problem, which isn't hard to fix. Hopefully you have a good spark so when you DO get gas, the car can run.