I recently battled these codes too, and finally found the fix. I read all kinds of forums, replaced different components, until I got out the service manual and narrowed it down to the wire harness going to the ECM from the ignition Ignitor.
In the engine compartment, attached to the firewall, is where the ignition Ignitor is. It is just about centered on the firewall. It's maybe 2" by 3" and about .40" high. Where the connection is, is where the problem was. There is flat connectors which slid into acceptors (about 4 or 5 all together). Those acceptors had sprung apart so there was not a positive connection. I got a small screw driver and closed the 'acceptor' connection a little. Just enough to make full contact. The P0303 and P0304 codes have NOT come back. It's been about 1,000 miles.
My car is a 1998 Subaru Outback with a 2.5 engine, or 25J.
