Never saw one on a tractor (other then mine...oil changes etc., never worked on a tractor), but on a Mercedes Benz 240 and 300 Diesels, we'd get glow plugs that were carboned up...don't remember the exact root cause (I was working at the shop to afford parts for an old Porsche i owned a few years back). The way it was described to me, the glow plug wouldn't heat the cylinder properly if they were caked up...heck, they all looked caked up to me. But the fix was to replace them. That always worked. This was also on high mileage engines, though.The lead mechanic always blamed this on cruddy fuel. We could try cleaning them with solvent...not too successful.
Steelfan's TC21 seems to be too new (or too few hours may be a better description) for this....but there is only a few things that will prevent a diesel from starting: no fuel (air leaking in system?), no air (filter clogged?), cylinder not making enough compression, the engine being off time, starter not cranking fast enough (check battery) or the glow plug or plugs not doing there job. Steelfan's tractor is starting, but not fast enough. First thing to check is to make sure air isn't entering the fuel system (most logical possibility is the fuel filter). Then, is the glow plugs doing there job? Pull them out and test them (need the manual). Compression? Engine should be down on power, or you could run a compression test (let a dealer do this unless you want to buy the equipment...diesel compression is too high to just hold the tester in the glow plug hole...these testers screw in).
That's about all one would want to check at home, unless you're a mechanic and knowledgable about diesels. DO NOT (!!!!) DO ANYTHING WITH THE INJECTION PUMP!!!!
Steelfan just bought the tractor...I'd call the dealer first (did you get a warranty, Steelfan?).
This is, in all likelyhood, a minor problem. There's only a few things one can try at home...or fix at home.