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If your car just dies like it ran out of gas the battery light and check engine light will always come on. Turn your key to the on position without starting and you'll see the same thing. It sounds more like a fuel delivery problem. Fuel pumps are extremely common on your car and the most common cause of of the condition you described. The other more uncommon reason (which I have seen more times than I can remember) is when the car overheats, the driver ignores the red temp gauge, keeps driving and eventually stalls out due to an extreme over heat and loss of compression. You will see the battery light and check engine light, only this time you will need to replace the engine. Hopefully you just need a fuel pump. On a side note: A problem in the charging system will never set a check engine light on your particular vehicle. If the alternator were the failure, all of your lights and instruments would go dim and the car would then stall. You would likely not get it restarted.
Your leather can be "dyed" by an upholstery repair person. They basically get resprayed, like painting a car, to look like new. If you have a good dealer their used car department will have contracted someone to do this on their used car inventory. Ask around the dealer. A service advisor might be able to point you in the right direction.
Your coolant level sensor is either broken inside of the expansion tank, the connection is loose or you have a broken wire near the sensor. All of these are very common on your car. As for the transmission, you can change the chip but you need someone to write you a less aggressive map. Most chips available aftermarket hang 3rd gear longer for "performance" reasons; not what you're looking for.
No special tool is required, only a little know how. The door lock button sticking out the top of the door panel will need to be removed along with a screw behind a circle cover on the opener lever. Then work your way around with a door panel tool or a flat screw driver carefully around the perimeter of the panel. Once the entire perimeter is unbuttoned and it seems like it should come off you then want to lift the door panel upward. It should come off. You will need to removed the black rectangle clip in the middle of the door and transfer it to the door panel when reinstalling. Be careful, there are several connectors behind the door panel that will need to be disconnected and reconnected when removing and installing the panel. Even a veteran BMW technician finds this a hassle. If you plan on doing repairs on your own vehicle I highly recommend a Bentley repair manual for your vintage BMW.
First thing to check is if the gear selector cable is connected to the transmission and is functioning correctly, especially if you cannot engage park. If this is okay you will then need to check to see if an axle has popped out of the rear differential or if the rubber drive shaft connector (guibo) has failed. If the problem still hasn't been found your assumptions may be true but can only be realized by having your local BMW repair facility diagnose this issue further.
The injectors rarely go out or need to be replaced on this vehicle. You need to go to a professional mechanic to diagnose your problem. You will not find a simple answer to this question online. If you haven't replaced your spark plugs in a while, it may be time to do so. Leaking valve cover gaskets can fill up the spark plug valley and damage coils causing your condition. The intake on your vehicle is known to leak at the rear crank case ventilation plate causing a lean condition,or you may have a cracked and leaking throttle boot. Any of these and many others will cause your vehicle to run rough. Save time and frustration and see a professional BMW mechanic with quality diagnostic abilities. Be warned though, more than one of the conditions described above may need to be corrected to have your car running properly again.
If the plastic trim piece that holds your driver's seat adjustment switch is broken or sagging, it is likely the connector for your seat switch has broken off causing the condition you described. The trim piece needs to be replaced when replacing the switch and connector to prevent this from happening again.
The bottom end of you engine is, what we like to call in the industry, bullet proof. It is a cast iron block and I have yet to see one that can not accept a rebuilt head. If there is no damage to the cylinder linings or pistons and no excessive play in the wrist pins or crank, then a rebuilt cylinder head should fix your woes. Cylinder head exchanges are readily available online for less than $1000. I have used www.headsonly.com a few times with good results.
Your 2004 325xi has front and rear open differentials. What this means for you is yes, you can drive it for a short time in this condition. BMW anti-lock brakes and traction control electronics can be very sensitive. All wheels and tires should be the same size as well as the same brand on each axle. Two different manufacturers may sell the same size tire but the circumference may be off enough to set a fault in the vehicle.
Hi Sam, Do not attempt to try to check the voltage with a meter! You will get a nice tingly shock throughout your body. 99% of the time the igniter is the culprit (the other 1% would be the xenon control module for the affected side). The head light will have to be taken completely apart to change the igniter. I would suggest the repair be done at a local high end BMW independent shop if the dealer is not an option.