Lots of good details in previous posts in this thread.

For not going into 2nd gear: I'd suggest removing the console cover and disconnecting the cable from the J-gate mechanism. Then you can determine if the problem is within the J-gate itself or the cable is not moving properly. A stretched cable is one possibility, or that infamous cracked plastic block in the J-gate. Make sure the mounts are secure at both ends of the cable. Be sure to read the TSBs in those previous messages.

For the no-start, there is a "transmission range sensor" on the side of the transmission, where the shift cable attaches. This picture, shamelessly stolen from eBay, shows this component on the US driver's of the transmission:




Take a look at the wiring diagrams here, near the top of the page:

JagRepair.com - Jaguar Repair Information Resource

Figure 04.1 shows the transmission, and 02.1 has the starter circuit. This sensor has two somewhat independent functions, as seen in the upper right corner of 04.1:

One function lets the starter engage only when the transmission itself is in P or N. This is feedback from the transmission, NOT the lever.

The other function is to provide feedback to the Powertrain Control Module as to which gear is selected. Once again, this is feedback from the transmission, NOT the shift lever. I'm not 100% positive, but believe this sensor also provides the feedback for the indicator lights on the J-gate.

When starting in neutral, does the N illuminate at the base of the lever? I'm pretty sure yours will. What about when in park? Does the P illuminate then? I'm thinking most likely not. Please confirm if those indicators are lighting up properly. That should help with further troubleshooting.