Upgrading from 3.5 to 4.0 with a custom driver would be a bit of a pain as the driver wouldn't work with 4.0 (the vmkernel went from 32 to 64 bit with the version change).

Well, sure enough, I just used the VM where it sat in the same datastore and added it to my ESXi 4.0 inventory. Started the VM up, and I can browse the web. It's now working, so I won't bother to dally with it any more. Again, thanks for your time and feedback. It's truly appreciated sir.

Thought I would add more findings to this, in the event that someone else is troubleshooting a similar issue. File transfers still seemed to be broken when transferring from VM to my physical machine.

I saw something in the vSphere client that I'm pretty sure I hadn't seen before. On the configuration tab, networking link, I saw my two NICs. I had load balancing enabled across the two NICs. I noticed a red X next to one of them during the file transfer (eventually it came back online, but it kept dropping off). I took that NIC out of the pool and rebooted the VM. Low and behold, transfers work fine now.