To test the ground, I'd first test the battery and chassy connection, to make sure the chassy is seeing the full ground. Do this with your ohm-reading function on the multi-meter. It should read no resistance. Then, take a similar reading between your amp'* ground wire (disconnected) and the chassy from anywhere in the back. It should also ready no resistance. If both those look okay, take a length of wire (ANY speaker wire works fine) and run it from battery negative terminal to trunk, and do a reading between it and the ground wire that is now disconnected from your amp. All should show no resistance, otherwise, you've more than likely got a poor connection.
When I do connections I usually use a fresh length of wire freshly stripped at the end, and screw it to whatever after rubbing a little of that corrosion stopping dielectric stuff on the end. Then if it'* done right the first time, it'll be the only time you'll need to do it.
Hope you get the problem figured out.
'95 SSEi, few electronic mods (and a stupid coupler)
HU (Sony MDX-CA680, European Ver; Sony 4x3-ways; 91, 93dB)
Yup, that'* ISU