I recently bought this car with a known defect: it had an auto gearbox fault. It would not drive forward, but would drive backwards. I am a DIY mechanic and have a lot of experience with big cars.
As I have previously repaired a BMW gearbox, (a ZF 4HP22 4-speed) common to Range Rovers, Jaguars and Volvos of the 1990's, I decided to have a go at repairing the 730i. The car was in near mint condition with 120k on it, and had full dealer service history too. Imagine my suprise when I found that only the selector cable had broken! It sounds unbelievable, but somehow it was pushing the selector arm out enought to engage the reverse and then neutral, but not the forward gears. How it got out of reverse is just weird, but I'm not complaining! Hell knows who diagnosed it in the first place, but if it was via a telephone call to a gearbox shop they would have suspected the box I'm sure.
I replaced the cable for £15. The car is a dream to drive: tight and quiet, as it should be. Everything is in tip top order except the aircon is 'empty'. It has two tappets that require adjustment, but these are straight forward to adjust in an hour, with just an allen key and feeler gauges when the rocker cover is off. This is the M30 3.0 six engine: a bullet proof engine, IF you change the oil and more importantly check the water level. If these cars lose a pint of water, they get too hot at the thermostat housing, and will not operate the temp sender (as it's no longer touching coolant). This overheats the engine, but doesn't necessarily tell you until a hose bursts. It gives symptoms of head gasket failure, but since the head cracks before the gasket goes, you're in for a wallet busting repair.
If your gearbox has 'slipped away' from forward drive and still goes backwards, then don't buy a new gearbox. Take out the old (a rotten job, but so is withdrawing £1000 from your account) and then unbolt the bellhousing. Pull it off, remove the front pump, and out comes a shaft that has a pair of small piston ring seal on it. You must change the seal, and the small 70mm set of six clutches held in by a clip on the gearbox end of this shaft. One or more of these six clutches will have failed: these control 1st gear. Also, the shims will need a change too, since they may have welded themselves to the clutches. These cost around £35 for the 1st gear clutchpack, and a new filter, for around £15 too. That's IT! £50! Take care with the front gasket, and reassemble. It will drive fine. Your slipping box will be OK in the other gars, so don't get cocky and try to change the rest, as you will regret going any further. These ZF 4HP24 boxes were good gearboxes, but a poor design; those shaft rings when worn will allow the front clutch pack to be 'in gear' ie at full contact pressure when in neutral. Did your car tend to creep a tiny bit before it went all 'slippy' when put back to neutral? Search the web for '4HP24' and read about it.