Todd, I havent heard of the underinflation causing an ABS or DSC failure to light up the malfunction indicator lamp on the dash. I hope your seller didn't tell you that. First place I would look into is having your codes read on your car by taking it to a mechanic or auto parts store with more than just the general scanner which typically only will read engine and tranny codes. Some people have had luck with the autozone reading 'enhanced' codes like the ABS stuff, but most have not. You may have to take it in to another mechanic who has this ability. To be honest, most will not have the expanded ability to read the jag codes, sorry to tell you that. If you were in TX, I could read them for you, or perhaps you can find a jag dealer that would read it for you for a small diagnostic fee. Anyhow, the reading will tell you several things. These cars have so many circuits/systems that are monitored, that it can really help you, or your service tech narrow down your search for what part might be affected. For instance, if a wheel sensor is going bad, the reading of the codes will tell you which one...it often is, or could be just a wiring harness to that sensor, or perhaps it is sooo fouled up with brake dust, that a good cleaning of that particular sensor will clear it help. Of course, after you do the repair or cleaning, you need to clear the code, which again...most people cant do with a basic handheld unit. If you really want to do it yourself, I recommend the AutoEngenuity scanner with the jag pack...you'll spend about $500 for it and the software, but you will get alot of use out of it during the ownership of the car. The dealer will charge roughly $125 for just a diagnostic...so it only takes 4 new trips to the dealer to pay it off. Each dealer is different, if you get a good relationship with one, those diagnostics may not find their way into your invoice if you have the work done in their shop, it just depends. I had a new gas cap installed for a small evap leak and the service guy grabs the code scanner, hooks it up, checks the code, clears it for me and tells me to have a nice day. Relationships are everything when you have a car of this brand, including ones with your service guys.
Good luck!

Edit - and with that AE scan tool, you can clear your own MIL displays.

 

Don't get too discouraged, you'll get these issues resolved. Not only do you want go hours down the road, so does your cat!!!!!