If you can, hook up an Amiga monitor to the 23pin video port. I've seen a few cases now where battery damage has caused output from the 15pin port to fail.
Other than that, you're on the right track. Cleaning up the battery acid should be your first priority. Isopropyl alcohol is a good cleaner for this job. Even if the tracks aren't damaged, per se, the presence of the acid on them can interfere with the signal. I once got a 4000 working again by simply removing battery acid.
