1994 3.2 XJ40 not starting after flat battery

Justin, first, welcome to Jag-lovers! Great bunch of folks on J-l as I am sure you will learn. Sorry to hear of your no-start issue. Here is a link to a VERY long thread (193 posts) chronicling Jag.Man’s journey chasing a no-start issue:

1994 Jaguar VDP No Spark - #185 by Jag.Man?

Post 185 (linked) sums up the resolution. Does your car have 7 relays on the right side of the firewall, with one of them having a white base? If so, that will be the Ignition On relay that could be suspect. You can swap that relay with the A/C relay (green base) as a test if you don’t have a spare.