I've seen this before on 2 different Eagles, it ended up having to do with electrical/ignition. This is the route to follow :
Check these :
- ground wire(s) - these WILL make an engine seem like it's dying and on it's last legs. Add a few grounds around on the car.
- starter solenoid - this is ALWAYS the first thing I check after grounds. I've had this make it look like the engine was dying, fuel pump bogging, plugs need swapping and even the timing skip. It's a cheaper than heck replacement, and I prefer the older ones rather than the new ones.
- distributor cap - remove it to make sure the rotor and cap inside are still good. Also ensure it's not swiveling around (causes timing issues)
- plug wires - use a timing light on each wire. A broken wire will cause a load of issues.
- plugs - alternatively, remove the plug and wire, pop the plug back into the spark plug wire and sit it on a grounded point, watch for a spark
If the plugs, distributor and wire look good check the timing. Some people have reported a skipped timing chain but I haven't seen it happen (even on pulled engines getting to run).
My guess is the solenoid, or the intake/exhaust manifold gasket blew a chunk. It will also cause these exact same issues. The carb can blow out the top if you keep trying to start it...that's normal.
Give that solenoid a few smacks and see what happens, or tap it while it's turning over.