Welcome to genvibe
You've replaced the starter, which would be the prime suspect, but the odds are really low that a new one would also be bad.
There is a wiring diagram for the starter circuit at
download/file.php?id=5873
You said you get 12.4V at the starter solenoid, is that when the key is turned to start? From the wiring diagram, was that the red wire or the black wire?
In the other thread (
viewtopic.php?t=49250 ) you asked about the ignition relay. One way to check that relay is if the wipers work when in the ACC or run position, but stop when you turn the key to Start
Both the starter relay and the ignition relay are in the dash, left of the steering wheel, on the top of the inconveniently placed under dash fuse block. You can access it by pulling out the little storage bin and/or pulling off the air vent/mirror control trim (just pulls out)
Here's a diagram of the parts location on the top of the under dash fuse block.
The starter relay is marked with the red arrow. The ignition relay is labelled as "IG1 Relay" A quick test of the IG1 relay would be to swap it with the power window (P/W) relay next to it. Can't remember, but from the location pic, it looks like the starter relay and the DEF (rear window defroster) relay are the same, so you could try swapping them to see if that has any effect.