I run windows 7 myself, build 7100, 64bit and have had no issues at all with D2:LoD - that said I don't play online, not that that should effect it anyway. Your symptoms do sound like a memory related issue though - either the drivers you're currently using are not great, or you have flakey ram I would think. I've had similar problems in the past myself and it almost always came down to the ram.
I would try updating your chipset drivers, assuming you're using an onboard NIC this should eliminate that possibility as well, and if you still get issues, then try running some memory subsystem tests. memtestx86 used to be quite good for this, though it does take a long time to run, and you can't do anything with the machine until its finished, since it runs below dos level.