'85 Thunderbird Won't Start

Went out to my Thunderbird turbo coupe yesterday morning to start it and it wouldn't start, so I started doing some diagnostics...

Checked the battery and topped it off with a charger.
Checked the spark and it seemed a little weak, so I replaced the coil pack. That improved the spark. But still no start. Car has very new wires, plugs, and new distributer cap and rotor.

Turned the key to on and listened for the fuel pump. Didn't hear a thing. Jumpered the fuel pump to the battery through the diagnostic terminal and the pump ran nice and strong.
Checked for kinks and clogs in the fuel line. Disconnected the hose going out of the fuel filter and ran the pump again, plenty of fuel. Did the same thing inside the engine bay and getting plenty of fuel there. BUT, only when I jumper the pump. The pump doesn't turn on at all when I just go to start it.

At the same time, even when we jumper the pump, the car still won't start. You can hear the starter trying to turn the engine over, and the starter sounds really good, but it just won't run.

I hooked a code reader up to it but didn't get anything.

Changed out the EEC relay.

In the past couple weeks I noticed a rough idle so I cleaned the throttle body and replaced the throttle control valve. Also replaced the PCV valve and the hose going into the top of it. Otherwise, nothing has been changed on the engine. Did a new timing belt a couple weeks ago, and had some trouble with the engine jumping time, but it's been running pretty well the past couple weeks.

Sorry for the long delay. Check the fuel pressure and also see if you have 12V at the pump with the key on. You should check the timing again.

I ended up sending the car off to a second shop, who discovered that the air flow meter was pulling down the VREF signal from the computer and causing the beforementioned problems. The engine runs, albeit badly, with the air meter unplugged.

I'm hoping this will solve the problem, as I've decided to bring the car home to do the work. Here's what I was quoted for them to do all of the work:

$358 for the diagnosis
$297.38 to replace the Mass Airflow Sensor ($211 part, $85.50 labor)
$171 for underhood repairs (resetting timing which had slipped, taping and repairing some wiring, etc.)
$171 to put the interior panels back on for around the wheel (where I had replaced the ignition switch, and the panels that had been taken out to get to the PCM.
Total Work Order $1039.27 (includes tax and disposable supplies)

I thought that for $500, I could change out an air sensor and put the inside of the car back together! If the new sensor doesn't work, I'll probably part out and scrap the vehicle.

I'd like to know why your timing keeps changing! You've had a lot of trouble with that. Are you talking about the ignition timing or the timing belt slipping?