Okay, put on your Diagnostic Hat...

Any ideas?

2007 Ford five hundred SEL Sedan 4D

Seller's Description

"New tires, good interior and exterior body all appliances are in operating order. Car will not exceed 20mph, oil leaking, could be a cheap or expensive fix being sold AS IS."

I won't click on any Facebook links, but it sounds like the two problems are unrelated.

Oil leaks are not terribly common from the engine, but the trans lines like to rust out.  That car is old enough that it probably has hydraulic power steering, which can be a real nightmare to service because of how it is laid out.

Won't go over 20mph suggests a fault somewhere in the accelerator pedal or throttle body (or wiring thereof, etc) to where the computer won't try to move the throttle, so it stays fixed at 15% or whatever neutral spring tension on the throttle body is.

Or the trans is broke and it won't shift out of first gear.

I'd run away just because I started seeing these have a problem where the end of the camshaft wears out and the water pump stops turning.  I also have not seen a Five Hundred on the road for a very long time, I think these two statements may be related.

CVT trans is borked, that's why it won't go over 20.

Missing from the pictures is a tail end picture which would show trunk badges.  

If it is awd it is cvt and run away.  There should be an awd badge.

If it is fwd it is 6 speed auto trans.  There should be no badge on trunk.  

If it is actually a 2006 the fwd could be either cvt or 6 speed (transition year) as Ford tried to improve reliability.  

EDIT:
A little trick I have used before...
I went to the Edmunds site where you can appraise your cars value.  One of the options is you can just enter your license plate and the site will pull the details of your car for you.  I entered the MO plate shown in the pictures.  The site came back with:

2007 Ford Five Hundred

SEL 4dr Sedan (3.0L 6cyl 6A)

VIN: 1FAHP24167G155706

This then seems to say it is a 3.0L, 6 cyl, 6 speed automatic (6A)

In reply to John Welsh :

Given the extreme unreliability of state DMVs... I'm sticking with its a CVT.

(My Boxster was classified as a Wagon by Oregon)

In reply to Javelin :

We ID cars by license plate at work.  What happens is the software polls the records for the VIN, and then the VIN gets decoded separately by whatever the software uses.

The only thing the state knows about my car is that it is a gray 4 door sedan.  The VIN decoder knows it's an AWD automatic with the B5254T4 engine.

I'm not familiar with the car, but if something is amiss, does the car have a "Limp Mode" to save itself?

In reply to stroker :

Buy it, gut the drivetrain, and do a RWD Coyote-powered conversion?

Quick Google search says that cats can and will plug and do this.  So will throttle bodies since drive by wire.

Vacuum gauge will tell you in seconds if it is a restricted exhaust.  Restricted exhaust might not throw a code since basically all it is looking for is O2 sensor function.

NOHOME beat me to it. I saw similar issue on a Honda Pilot, where a berkeleyered cat would flatline it at 2000 RPM.

Recon1342 said:

In reply to stroker :

Buy it, gut the drivetrain, and do a RWD Coyote-powered conversion?

I would like to subscribe to your newsletter

In reply to NOHOME :

Restricted exhaust can definitely throw a code on a drive by wire Ford, and cut throttle operation.  If it sees the wrong airflow for the throttle opening, it can throw a snitfit.

4cylndrfury said:

Recon1342 said:

In reply to stroker :

Buy it, gut the drivetrain, and do a RWD Coyote-powered conversion?

I would like to subscribe to your newsletter

I mean, yeah.. it might take a bit of fabrication, and lots of cubic dollhairs, but think about it:

Tube-Frame RWD grocery-getter from heck!!!

Pete. (l33t FS) said:

  I also have not seen a Five Hundred on the road for a very long time,

...and this happened today

Recon1342 said:

4cylndrfury said:

Recon1342 said:

In reply to stroker :

Buy it, gut the drivetrain, and do a RWD Coyote-powered conversion?

I would like to subscribe to your newsletter

I mean, yeah.. it might take a bit of fabrication, and lots of cubic dollhairs, but think about it:

Tube-Frame RWD grocery-getter from heck!!!

The rear suspension is pure Volvo P2 and the front suspension is halfway between P2 and Flex.  So the obvious answer is to swap a Volvo five cylinder drivetrain into it.

Better yet.  Five Hundreds rusted like shipwrecks, Volvos did not.  Look at the picture of the Ford while buying a Volvo S80, consider it swapped.