If it has a rod knock, just stop driving it and pull the motor. No sense junking the motor you have.
>My understanding is that it’s not worth the price to rebuild. The car itself has 220k on it, and I don’t have a shop or tools for a DIY job.
Codes are only present when the computer detects a fault. No fault detected, no codes stored. Mechanical problems are hard to detect because there is no sensor specifically dedicated to each mechanical part. Is the "Check Engine" light on?
>Check Engine light is not on; it’s just not running smoothly, so I thought it might throw some codes.
Have you tried draining the oil? If coolant has leaked into the oil pan while the car was not running, it wouldn't get whipped into a brown sludge ... it would settle to the bottom more or less intact. So if you drain a little oil, the first part should come out watery. If it looks fine, then maybe it's not leaking when parked.
>I have not drained the oil to see what’s in the bottom of the pan, but the oil on the dipstick has always looked like straight oil; not a hint of milkiness, even after driving. Also, there’s been no noticeable coolant loss.
You say the engine was replaced before? I wonder if it was botched in some way?
>That’s what I was told. Used car, so who knows for sure! For all I really know, the seller lied about a new motor, because the car has 220k on it. Or, maybe a botched replacement. Don’t know.
What do you mean that the engine runs rough at higher speeds? Higher car speeds? Higher RPM? Under load? Free revving in the driveway?
>I mean the motor starts shaking the car when parked in the driveway, when I get up to about 1800 RPM and above.
Have you checked the timing?
Have you checked the spark plug wire order?
>I have not checked the timing or the wire order. I’m sure I can find the information on the wires, but have no experience or tools for checking timing.
Where does this light knock appear to come from? Exhaust? Engine bay?
>Best I can tell; engine bay, passenger side, near the firewall. It does speed up to match engine speed.