I have a Miller Big Blue 251D and while welding it died and won't restart.

What is the question?

Here is a video to help you out. Good luck with that. https://www.youtube.com/watch?v=HzhafVQkqx0

Which windings? And what is the serial number?

Try here
https://www.millerwelds.com/support/manuals-and-parts

Have you stripped and cleaned out carburettor?
sounds like a blocked idle jet?

Check this link for pages that show similar images for the serial number:

http://www.machinerytrader.com/listingsdetail/detail.aspx?OHID=9473215&dlr=1&pcid=2863125 machinerytrader com

The manufacturer's repair manual for the Miller Big Blue 400D CC Duetz F3L2011 engine is known as the "Miller Big Blue 400D CC/CV Diesel Engine Driven Welding Generator Service Manual" (part number: 907596). It provides detailed information on troubleshooting, repair, and maintenance procedures for the engine and welding generator.
This manual can be obtained from Miller Electric or an authorized Miller distributor. It can also be found on the Miller website, you can download it from there.
It's important to refer to this manual for specific instructions and guidelines for troubleshooting, repairing, and maintaining your Miller Big Blue 400D CC Duetz F3L2011 engine.
Please note that this manual is for the Engine, you should have a separate manual for the welding generator itself, it's important to refer to the manual for the welding generator for specific instructions and guidelines for troubleshooting, repairing, and maintaining your Miller Big Blue 400D CC welding generator.

the same thing happened with my 280 nt . I've just spent almost a grand on pc board . when i picked it up from roberts oxygen it worked . when i got it home , no weld output again. motor and generator works great though, but that's not why i had a welding machine. i believe something is grounding it out , and possibly blowing the pc board . . anyone want to buy it ?

Probably your machines overloaded. Check your fuses F1 and F2 and if they are open replace them.
Both fuses are located at left hand side of machine, open it and you will find them on the bracket.
Check your owner's manual for more info about fuse replacement.

go to miller .com a u will get free manual there good luck