SOLUTION: Replace Cold Start Valve (CSV) or (more likely) the fuel line to it.
HOW DO I KNOW? Have had it on my cars, and it can burn you to the ground.
DIFFICULTY: Rather easy but a bit 'fussy'; here's my old post swiped from the alt.autos.bmw Usenet forum:
I started at 1:00 and finished in one hour flat, including backing the car out and fetching tools and the hunk of fuel hose left over from the last time I did this on a different car (if you ever saw my place, you'd understand).
Begin with about 18" of fuel line. The OEM BMW line is 8mm x 13 mm. SAE 5/16" i.d. line is specified as 7.9 mm and it's a lot more available on a Sunday afternoon. I'm not quibbling over 0.1 mm. However, you need SAE J30R9 (high pressure) line! If you ask for it by name, you'll probably confuse the clerks, so ask for "fuel injection hose" and then look to see what it says on it. If you buy it from BMW, you'll get the right stuff.
TOOLS are few and simple. I used 1/4"-drive 6-point sockets in 5, 6, and 10 mm sizes. A small slotted screwdriver can substitute for some of these on the hose clamps, but it's a lot faster using the sockets, especially if you can't see 'em. In addition, you can cobble together a few 1/4" extensions or use a nutdriver for more length in a few spots. You'll also need an X-acto (#11 blade) or other equivalent knife or scalpel. That's it.
Begin by disconnecting the battery (10 mm). You'll be working in close proximity to the starter while leaning over the fan from in front of the car, so it's purely a safety thing. Next, remove the big rubber air intake boot over the top of the engine. This is two ~4" diameter hose clamps (6 mm drives on mine) and three 'push-on' connections for vacuum thingies and the idle control valve at the back. As you're replacing the hose clamps later, you can pay attention to the best locations for future removal.
Disconnect the idle control valve's bottom hose from the manifold end, not from the valve. This gives you needed access, or at least vision, to the cold start injector (CSV) underneath. Then, unplug the electrical connector (push down on the spring wire) and take the whole mount and ICV assembly off the valve cover bolt (10 mm). You can now see both ends of the cold start injector line. The top one is a no-brainer, coming off the bottom of the fuel rail right behind the ICV's former location (Aren't you glad I told you to take that thing off?), but it appears to be plastic that you don't want to break by yanking it around, so just loosen the hose clamp for now and slide it down the line off the joint.
Your real challenge is getting the other end off. Depending on where the previous installer left the hose clamp, you've got to work your 5 mm socket in there (unless said installer used another size clamp) and loosen that clamp. You'll quickly see why you probably don't want to do this with a screwdriver. On this most recent one, I stuck a nut driver with a 3" extension and a deep 5 mm socket up through the middle of that manifold brace that runs down to the bottom of the block. I did this almost entirely by feel once I knew where the clamp screw was pointed (the wrong way!) , working from the front of the engine and leaning over the radiator with my right hand under the manifold and an occasional look and check with my left hand from the top of the manifold. When it's good and loose, slide it back off the joint.
Now, it's scalpel time! You can easily see the connection from the right side of the car. Approach this as if you were performing your own vasectomy! Cut it lengthwise to split it and cut it crosswise to allow the split to be opened almost all the way around the hose. Work slowly and gently and be aware that you'll spill quite a bit of fuel as the fuel rail pressure empties through your cuts. The hose will be sticking to the plastic (Hey, it's probably been there a minimum of 15 years!), so work slowly at it and be gentle. It'll eventually come loose. Cut through the top fitting the same way. Remove the old line whichever direction seems convenient. The plastic protection grommet in my manifold fell apart, but I figure this line doesn't move much and it should easily outlast the car's remaining years, so I ignored it. [Addendum: It costs all of 65 cents at your BMW dealer ...]
DO NOT CUT YOUR NEW LINE TO FIT! It's about twice the length of your original at this point. Put a hose clamp loosely on it (but just tight enough to stay in place) an inch from one end. Once again using your surgeon's skills but not being able to see at the same time, work this end onto the cold start injector. [Be gentle! The injector body/nipple is plastic and you do not want to break it! It costs approximately $50 and it is a Royal PITA to change. If you do manage to break it, or it is the part that's actually leaking, there are only those two little nuts holding it in there. Have yourself a ball and don't plan on going anywhere soon ...] After you've gotten it there, I suppose it would be better not to tighten it immediately as I did, but that works, too. If you have trouble getting the line started, you might want to try chamfering the end of the line slightly with a countersink drill bit (Tip courtesy Lotus72D).
Once again not being able to see, you need to work the new line back into the original location without tangling or looping it around any of the lines, wires, braces, and hoses underneath there. It took me three tries over about two minutes. Not as bad as it could be. While you're doing this, you do not want to pull or twist on your injector fitting. Because mine was already tight, I had to add one extra attempt to my replacement routing because I had a half-twist on the line. A loose fitting might have allowed it to rotate. OTOH, it might also have come off ... At any rate, you'll quickly see why I told you not to cut it to length.
After you have the line happily in place, but far too long, then you can cut it to fit to the fuel rail connection. Tighten the line clamps remembering that it's still plastic under there. There's not so much pressure they have to be 'ape-shit' tight. 'Snug' is plenty. If it leaks a little, you can tighten it later. Replace the stuff you took off earlier, reconnect your battery, and fire it up. Obviously, it'll crank a second or so longer to get the fuel rail refilled. Then all you have to do is reset your OBC and recode your radio. You do know the radio code, don't you?
