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Try erasing it with a scan tool if disconnecting the battery hasn't worked. But it is possible that the cam and crank sensors just didn't solve the problem. What were the codes? Where did you buy the sensors?
I believe this engine has the timing chain vs belt. Try removing oil filler cap, have someone else try to crank car while you look inside the oil filler cap hole to see if anything (cams) are moving. But what makes you think its the chain?
Try cleaning throttle body and checking for vac leaks/restrictions
Would advise trying to isolate the cylinder that is misfiring via scan tool if available. Replacing all coil packs may get expensive and may or may not fix issue. There are MANY variables, that can cause p0300. Timing could also cause it along with faulty ignition parts. . If you can isolate issue to 1 cylinder that would narrow things,down a bit. Maybe injector, compression issue.
Could be maf sensor or vac leak. But just guesses without further diagnosis. If you have a,good scan tool you can check fuel trims.
make sure the connections are tight where he installed the pushbutton start. just a though...what if a improper connection is causing bendix to not fully operate. doesn't hurt to double check the work. aside from that though, I agree with removing starter. id physically check it and teeth on flywheel. HTH...had to edit this. didn't realize you have new starter. ok did the scraping noise happen immediately after the new starter put in?
you can try doing a thermometer test for the catalytic converter (this may be the issue). get an infrared thermometer (from harborfreight or the like), check temp before and after the cat. the temp at end should be hotter than at the beginning of cat. maybe 100 degrees or so. do this once the car is hot. Ive seen the cats on tauruses fail often. just something to check that wont cost a lot to do. and make sure the o2 sensor connectors are good n tight and cleaned (connection side). HTH
Hopefully everyone had a wonderful day/vacation. In regards to "fuel in oil", try looking into the fuel injectors. It is possible that they are leaking.
Have it smoke tested for vacuum leaKS. also can be caused by "soft" hoses that aren't "leaking: but are collapsing which will "choke" the engine. pcv hose,etc.
Cam timing is very good answer. Can cause plugs to get wet due to not firing in correct order. Compression check after that won't hurt.