We've been working for a couple of months off and on on a 1987 Jetta
GL 1.8 8-valve gas that refuses to run. I inherited in from a guy who
told me he drove it for a while and then developed a head gasket leak,
so he took the head off and had it surfaced, reinstalled it, and was
never able to get the car started again.

I thought it was going to be a simple problem, because the guy had
really screwed up the engine timing. The cam gear has a dot on both
sides, and he had lined up the outside dot with the front of the valve
cover, and then had changed all the plug wires around to try to
correct for being 180 degrees out. So, the first order of business was
to line everything up right and reinstall the timing belt. The two
marks on the harmonic balancer and the intermediate sprocket that
drives the distributor are now correctly lined up with one another,
and the valves are set to TDC on number 1 with the inside alignment
dot (the one on the tooth, not the one on the valley) lined up with
the top corner of the valve cover. The distributor is now pointing to
the engine block, and the plugs are correctly lined up 1-3-4-2.

Along the way, we discovered that the fuel pump relay was shot and the
fuel filter was clogged, so we jumpered around the relay, and replaced
the fuel filter. We're now getting a good conical spray of gasoline
from all four injectors.

It still wouldn't start, so we tested compression and discovered that
the #1 cylinder was down to 50 pounds, and #4 was sitting at 75
pounds. We took the pistons out, found all the top rings stuck and all
the rings on #1 an #4 stuck.  We cleaned everything up, re-ringed
them, cleaned up the badly carboned-up cylinders, and reinstalled the
pistons with new con rod bearings. While the top was off the engine, I
replaced the badly shot o-rings and shrouds on the injectors and put
in new plugs, properly gapped.

At 11 p.m. last Friday night, after a long evening of putting
everything back together, we attempted to start the car. We filled it
with oil and coolant, hooked up the battery, got in, and twisted the
key.  Exactly the same result as we had before.  It cranks perfectly,
starts backfiring as soon as there's enough gas to do so, and
absolutely refuses to run.

With all the work we've done on the engine, I'm convinced that's not
the problem any more, but that it's gotta be something hanging off the
engine. So, what? Hall sender? Computer? I don't know what to try
next, although pushing it off a cliff is beginning to look pretty
good.