Land Rover Discovery TDi 1 - I hooked up the battery with the polarity reversed then I reconnected it the right way but the engine will not start, not even the starter.

Hi welcome main problems are the abs valves causing the 3 dash lights (search 3 amigos online) a really badly sited compressor can cause air suspension models to fail giving the bags a slow leak the V8 is a solid engine but can have radiator expansion tank and cap failures
the other issue is electrics windows and door looms are problematic

Useless site...

The ignition system is controlled by the ECM. Check power at fuse box in on right side under dash. Check fuses right side engine compartmentlower dash panel if all OK check power to ECM located right side "A" pillar in alloy box. this unit could be faulty if no spark at coils, assuming they have been connected correctly. may have to get tested for codes at L/R dealer or someone with test tool. Another source of problem may well be flat battery in transponder key. The indicator light on the dash willflash rapidly for 10 seconds if the vehicle has been unlocked with the remote and the drivers door is opened if the battery in remote is getting low

i had the same problem. It was my battery. the battery is almost dead or you need a higher cold cranking amps. try higher than 700

check the wiring connections from the battery to the solenoid to the starter. also check the ground from the engine to the chassis

You can try unhooking your battery and hook it back up

LAND ROVER DISCOVERY II DONT HAVE FUEL FILTER, ONLY HAVE PRE FILTER IN THE FUEL PUMP

dust in the switches!

Have you checked the High-Low ratio lever.  Half-way between High and Low is a Neutral, so no drive to any axle even if a gear in the main box is selected.
Try locking the differential.  If this gives you drive, then it might be a final drive (half-shaft) failure.