Transmission problem

Hello and good afternoon i have a 2003 jaguar xj6 that has developed a fault but i have no lights or warnings on the dash.
1 gear shift stuck in park
2 parking sensors going off when stationary and nothing near
3 no light on j gate
4 stuck in sport mode
5 gears stick or jump in to gear

It seams like an electrical problem to me.
But the garage seams to think a transmission flush will sort it at a cost of £350+vat and they said they might have to do it twice and if that don't sort it then change the plates.

I've asked them to check the fuse box in the engine bay and check the solenoid in the transmission but they don't want to listen and telling me it doesn't have a solenoid in there.

A little help would be appreciated guys

Thank you kindly nigel

I would not start with a flush, not going to solve the issue with the jgate. Find a shop that has IDS/SDD or equivalent factory diagnostics, they should be able to communicate with the jgate module itself and see what is going on. If no comm, there's your issue.

Another common fault to check for was the shifter cable physically coming loose from the side of the transmission. There are 2 bolts holding it to the left side of the transmission. But the lack of the jgate indicator leads me to think the issue is electronic and with that module.

Thank you kindly it's very much appreciated will check them out]

One bolt fixed mine. No charge