I would say (also having multi-monitors) that a lot of older Direct X games can not handle having multi-monitors. You have to completely disable the monitor. Just switching primary and secondary. They get confused. I have 2000 and have experienced this several times with the games written for older version of direct X. I even have some related errors with playing Sims. But Diablo II seems to handle it right.
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guardian__J
MKIIa 20g Smoke