E39 not cranking

I have a 2002 E39 530i that will not start or crank. Lights come on, fuel pump engages but starter will not turn with key.

Last week I left my car outside in 10-30 degree weather for a week while I was out of town. When I came back "check coolant" was illuminated on the dash. It had trouble starting but with a little gas it would start and run fine. Still had trouble starting it for two days, but it ran and then the traction control light came on and stayed on. Then when I tried starting the car it again had trouble but was running really loud and rough this time. An OBD2 gave me codes P1083 & P1085. I tried driving it back from the auto shop to my house and it was spraying white fog from the exhaust and running rough again until it finally stopped on the side of the road. It would start but not run and eventually wouldn't start or even crank. The battery has over 12volts. I can hear the fuel pump come on. It has plenty of oil and coolant. Starter doesn't make any noise. Interior lights and headlights come on.

I've treated this poor car like ****, is there any hope I can get it running again? Im in school and need to get another year out of it. PLEASE HELP! Thanks

The 1083 and 1085 codes are indicating the mixture is lean. Look over all of the air ducts going into the engine for cracks. Also look at the DISA valve.

As Jim said. I would bet DISA as the freezing weather always seems to kill them. Winter is our biggest time of the year for the DISA Valve.

"The battery has over 12volts" How much over 12? How did you measure it? It must be a MINIMUM of 12.5 after setting overnight. A fully-charged battery measures 12.6-12.7.

Before I did anything, I'd charge the battery overnight at a 6-10A rate, then observe the operation. If it's more than several years old, it may be dying.

Does it at least make 'click-click-click' sound? Or complete silent when you turn the key?

if it was spraying white fog, that usually means coolant is burning in the engine. Maybe your head gasket is in need of replacement.
open up your drain plug and see if coolant comes out....