Sorry for stupid suggestions

My bike went through various issues which I sorted all out, and then it was stolen! 1VJ model so kick and electric start

With a low (or ailing) battery the electric start was useless, turned it over but wouldnt start. So try hooking up through Jump leads.

Its pretty warm now, so I would imagine trying a warm start procedure: Turning it over with throttle closed and choke closed for a minute (three or five kicks) to get fuel out of system.
Allow to rest.
Establish compression stroke, then give a bundle of throttle, no choke and one mother of all kicks! or electric start with a full battery and jumper cable attachments.

If that doesnt work, then try throttle closed and choke full blast. these bikes are temperamental when it comes to the balance of throttle and choke usage But they do eventually teach you how to understand them.
Never be gentle with the kick start!
Have you got the decompression lever in the correct position?

Other ideas:

>Air intake blocked, it shouldnt be but some kind chap may have added a rag to the inlets to prevent dirt ingress.
>The Main fuse... has it tripped?
>For the sake of the exercise are you starting the bike with the side stand up?
I really believe that the problem is around the sidestand cut out.
Side stand cut out switch?... check thoroughly, Even try starting with the side stand up, clutch in, and in gear, as well as out of gear, it could be picking up a false neutral.
>Rectifier and Regulator cables all connected.

> On the choke front it is supposed to spurt out more fuel from the one choke than the other at low throttle openings
Then more in the previous lower one at full throttle.

If you have fuel and a spark there will be fire. If there is no fire then its electrical.
>I have no technical XT single cylinder intelligence behind this statement, so dont abuse me for the inaccuracies
Is the timing chain set correctly, you dont mention whether it was a complete engine and gearbox swap, or engine only swap, and have you retained the Kick start?

Cheers G