I think I have a couple different issues happening currently.
About a month ago the car started to sputter like a lawn mower with a dirty filter but only in park. no problems with acceleration or surging. Changed the plugs and wires and ran great. this week the car started doing it again, this time started to overheat apparently was very low on antifreeze, haven't noticed or seen any antifreeze leaking. filled the radiator and reservoir. Car wouldn't start initially waited 45 min fired right up. Same problem with sputtering. however I lost reverse and D4. Drove the car home in D3. I thought it might be the EGR valve. This car doesn't have a EGR valve.
Some odd things I have noticed:
Air filter looks brand new, and its been in the car for 6 months.
Oily substance under the valve cover on both sides of the engine.
Oil is black but not soupy like you would see if the head gasket was bad.
No engine light.
No green light around D4 when you try to put it in gear. Red light around Reverse
The car has 275K miles on it.
So I'm hoping and outstanding mechanic can guide me to the light.

 

What normal maintenance has been done?
when was it done?
what have you done to start diagnosing?

 

The transmission is mostly mechanically controlled. I don't think there is anything electric that would prevent the car from reversing if the linkage is in R and the engine is running. Check the shift cable also the fluid level in the transmission. The lights on the dash are controlled by a switch inside the car at the shift lever, they don't tell what is going on at the transmission. The D4 light is likely burnt out from years of driving in D4.

As for cranks but won't start, the first thing to check there is (during a time when it will not start) to turn the key on but don't try to start, watch for the check engine light to come on and go out like it should, also the fuel pump should run and then stop. If that works, check for spark next.

 

maintenance is not as regular as it should be. it gets oil changes/filters at the recommended mileage. just changed the wires and plugs when it started acting up the first time. Couldn't tell you the last time the transmission was flushed , tranny oil still looks good not burnt. I intially thought it might be a vacuum issue (it still might be) found a hose with a cut in it. will replace. Also think I have a valve gasket leak. which in the process of replacing.Will definitely help with the stuttering. Still doesn't solve the issue of where the hell my anitfreeze is going or the trans issue. no radiator leak or hose leaks that I have found.
As far as the trans. it would go into D4 with green light around it but then after about 5 sec it would drop out of gear like you were in neutral or the clutch was slipping. its a automatic never had a issue with anything trans related with this car. my experience with trans issues is usually are a build up to, slip here hard to get in gear, hard shifting. I have none of that.