James,
What type of monitor did you use when the colors went funny? The best thing to do first with old electronics behaving badly is getting a can of contact-spray. This spray cleans electronic contacts. Apply it to the connector-pins of the cable and re-fit the cable, see if things change. If not, continue below.
It could be that the cable you used to connect the Amiga to the monitor has been internally damaged (most chance of it being damaged at either one of the connectors). This can be checked by plugging the cable into the monitor and the Amiga (turn both on) and gently 'wiggle' the cable a bit, while holding the connector steady, just behind the connector of the monitor. If no influence of that action can be seen on the monitor do the same just behind the connector sticking into the Amiga. If again no influence you'd be checking the connection between the connector of the cable and the ports in the monitor / Amiga.
These ports can be checked by very gently wiggle the connectors a bit. Again check for any influence. If there's any influence at the monitor or the Amiga the ports need re-soldering.
On the rolling issue... The oldest model 1084S monitors have a set of three or four turning knobs at the back-side of the monitor, near the 9-pin connectors. Play a bit with those and see if it helps.