03 Jetta P0672 & 4 codes still thrown after new plugs

My car wouldn't start recently and upon checking the CEL there was P0672 and p0674. I consulted the mega thread but haven't read it for fully.

I tested the plugs with a multimeter and plugs 2 and 4 both tested at a very high resistance so I replaced all 4 with Bosch 0250202022 plugs. I attempted to erase the codes but the scanner kept saying "Erase failed" so I disconnected the battery for a short period to reset the computer and tried starting it again.

The car still wouldn't start and threw the same codes but all 4 plugs tested within the acceptable range. I'm not sure where to go from here to be honest..

Are the codes somehow preventing the engine from being able to start up??

I'm assuming you meant P0674, not P0674 above.
The GP code should not prevent starting.
I don't think you need glow plugs in Florida, it's not that cold is it?
If no other codes are there I would check it the Anti Shutter Valve is stuck closed.
It's attached to the intake manifold where the air go in.
There's a vacuum servo that pulls it closed for a second or so when you shut the car off.
Engine usually cranks faster also.
If not, there's a clear fuel line from the fuel filter to the injector pump.
Look at the highest point and there should be a small bubble in it.
If not you may have an air leak in the fuel system and lost prime.
Do NOT try either to start the car.
Good chance it may do engine damage.

You are correct, I edited the post.

It's been getting down into the 40s a few days this week so it's actually been pretty chilly comparatively but two of the plugs tested bad so I went ahead and replaced them.

My car doesn't appear to have an ASV as the previous owner had a race pipe installed. http://imgur.com/gallery/nczPBGJ

The clear line on my car isn't very clear anymore but I'll see if I can determine whether fuel is in the line or not. I recently had the car in the shop for timing belt, resealing a leaky fuel injection pump, and some suspension work but it must not have been apparent then...

I'll go try to check the fuel line and see what I can find. I have been trying to start the car after changing the plugs so I hope I haven't done any damage.

After looking at the line, it appears to be dry of fuel. I will probably give the shop I took it to a call and see what they say. It was a recommended shop from this site so I'm sure it isn't due to incompetence.

I'll have to look into diagnosing this line being clear. I can't imagine the fuel would have gelled with the temperature; I'm not sure how much winterization would affect that.

Not fuel gel. Assuming you drove it after the pump seal. Sounds like perhaps there's still a leak and your fuel system has lost prime.

My fuel line is yellow also.
I often have to use a small pocket flashlight under it to see how much bubbles are in the flow.

Was the car sitting for a while before you found it wouldn't start?

How long ago was the pump work done?

There is a plastic tee on top of it.
It has been known to leak air through the O-rings in it and occasionally I have read it just leaks air for no visible reason.

If you are still getting the same codes for the glow plugs then the harness plugs could be making a bad connection.
I had that problem when the car was just out of warranty.
I tried pinching them a bit but it did not help.
I replaced it and haven't had trouble with it in over 10 years.
I have read some have wrapped a bit of aluminum foil over the tips of the plugs and that fixed it.
I would use heavy duty foil if I was going to try it.

There appears to be fuel in half of the clear line on the injection pump side but is dry on the filter side; does that mean it's lost prime as well?

The car had only sat 3 days before I found it not starting. The pump would had been done in the middle of December by a shop recommended on here.

Thankfully I was able to erase the codes and they haven't shown back up so that may no longer be an issue. The car has now been sitting for close to three weeks not running; I'm starting to get worried about other issues arising from that.

Reading single clear fuel line has giant air bubble. Problem. You may need to purge the pump, but you might try just doing the 4 injectors. Loosen all 4 maybe a quarter turn, put down some rags and crank. You should get a nice spray fairly quickly. If not purge the pump from the outlet. You may need to repeat just one injector. Once you do get it running, you'll want to track down the leak.

The line being half full leads me to think you have a leak also.
Do you know what seals the shop replaced on the pump?

If you don't get a good spray from the lines you need to prime it.
Normally you use a hand held vacuum pump to suck the air out from the return line going back to the filter.

I always wondered about using a small funnel to fill the pump and fuel filter.
take the line off the back of the filter that gets fuel from the tank.