Injection pump fails on cold mornings

Hope I have not overlooked a thread on this, but here goes.

2003 Jetta TDI, for the past 2 to 3 years it will not start on cool mornings. 2 years ago one shop said it needed the injection pump replaced to the tune of $2k, did not replace it, as car started when I got there, took it to the house and it behaved fine, car ran fine with several long distance trips for the next year. It acted up twice last winter on cool mornings, but always in afternoon, go out spin motor over for a 2 sec burst, on the 4th or 5th spin it starts up and smooths out.

A couple of days ago it was cold, would not start, had it towed to shop, by the time it got to shop it warmed up and ran fine. Finally this morning it failed to start as it was cool. And of course they want to replace the injection pump, timing belt and water pump. Timing belt and water pump have less than 3500 miles since they were changed last

So I guess I have to question if it is only seals on the pump, is it rebuildable or do I really need to lay out that kind of cash for a new pump? I can't think of anything else that could fail on a pump due to temp except seals.

Have you replaced your fuel filter?

Florida doesn't get cold enough to account for "cold start" problems. Have you had a shop check the injection timing? Too far advanced or too far retarded = no start.

Sounds like BS to me.... check for an air leak on the inlet side.

what do you call "cold" at your location? above 40F?

I agree on checking timing. Does the shop have VCDS?

When was the belt done?

Seals would not only affect winter cold starts.