First off, have you taken it in to the dealer yet? The sensor light does go on when it reaches an inspection point and can only be turned off by the dealer.If so, what do they say?

Really, only the BMW dealer can reset the check-engine light?
I understand the lights in my newest vehicle are all user resettable, but maybe not a check engine light. My new vehicle has displays to tell you to change the oil, I know that can be reset, I don't recall anything about a check engine light in the owners manul. If it has one, it is a Chevy Colorado, I'd bet a repair shop with the right GM tools can repair/reset the Chevy, one doesn't have to go to the dealer.
NJ will not pass a car for inspection with a check engine light on, I understand.

Did you consider the possibility that you may actually have the problems indicated by the codes? The check brake fluid light on the instrument panel is separate from the codes from the engine computer. That would be due to low brake fluid of a bad switch in the brake fluid reservoir. The codes from the engine management computer are different, and you'd need to have those checked by a dealer or other shop who can inspect the systems and determine whether there's actually something wrong or whether a sensor is just bad. Often the light can be turned off by disconnecting the negative battery cable for a minute or so, especially on a '95, which probably won't have as sophisticated a computer as a newer vehicle.

The light can be turned off by disconnecting the battery but unfortunately comes right back on when the car is started again. The DME computer code, I've heard, can masquerade as other problems because everything is tied into that. What else can I check that may set off that code? Thanks.

You might want to search online for some BMW forums, or get a service manual for this particular car. What does DME stand for?

DME is BMW's fancy word referring to the computer. I'll take your advice and check out those forums. Thanks again.

Jerry said "Really, only the BMW dealer can reset the check-engine light?"

Resetting a check engine light, and actually performing the required diagnostics, and repairs are two completely different things. In an answer, yes it is quite possible that only a dealer, or an independent that wants to specialize in BMW's will have the tools and equipment necessary to perform the service properly. FWIW, the BMW factory tool, which includes BMW's factory service information starts at $18,000.00+ and has 1/4ly updates that run another $2,000.00 a year. No I won't be buying one, ever...

"My new vehicle has displays to tell you to change the oil, I know that can be reset,"

Don't wait for that system to tell you when to change the oil if you want to keep this vehicle a long time... JMHO..

"I don't recall anything about a check engine light in the owners manul. If it has one, it is a Chevy Colorado, I'd bet a repair shop with the right GM tools can repair/reset the Chevy, one doesn't have to go to the dealer."

Yes a shop with the "right tools" can support that vehicle. As much a factor of market share, plus desire the GM TechII scan tool is widely available, and a number of the top independent shops have stepped up to the plate and purchased one, (approx 1 in 100 independent shops). From there it's a business decision whether or not to purchase reprogramming software and updates, and you will likely only find one in twenty shops that have a TechII are involved in flash reprogramming. There are many aftermarket tools that have varying level of support for GM vehicles, most will support GM 80% of the factory tool or slightly better. For the most part this is what you will find most shops using, one of the Snap-On scan tools. (MT2500, or MODIS, SOLUS) Vetronix Masteretch, (Vetronix made the TechI, and TechII tools for GM), OTC Genysis, Nemysis. Some of the most elite of shops will have more than one of these tools. My GM coverage has me using the TechII first and foremost, but I also have the Vetronix Mastertech, and the Snap-On scan tools which I owned prior to the purchase of the TechII, and end up keeping them up to date because the manufacturer bundles the updates. Average cost per tool is $1100 a year for updates. We'll talk about Ford, Chrysler, Toyota, Honda all of which I have factory tools and support for in some other post....

BTW I do have software support for BMW, but it's not factory level, but it is O.E enhanced. Essentially that means it's not just the generic OBDII that the EPA requires under the clean air act, but it's certaintly not the same as the dealer uses either. It's not beyond the possibility to expect I could start into a diagnostic/repair attempt only to find out the tool ($4,000.00) does not support the particular problem the car is experiencing.....

BTW, without going into detail, on one hand you would think every shop would jump at the chance to have the correct tools to do the job, but the reason they don't has to do with the tug of war with many of the customers that occurs as they attempt to run a profitable business. After decades of not turning the kinds of profits that an independent should make, the result is an ever snowballing collapse in the number of independent repair shops, simply because they are not tooled, and trained to keep up with today's cars, and they didn't know how to deal with the situation that is created by (or should I say outlined by) the previous post you and I were involved in.....