marcs41 has a good start to your nic problem -- I think. The cards have not swapped, one of them is not configured properly. I am guessing that you are using pci cards. If you are, the most common problem would be an IRQ conflict. Because the first card failed when you installed the second, it is somewhat safe to say that those two cards are fighting for an IRQ. Could be that one is fighting with something else, but not likely.
To find out what the problem is, right click on the device with the problem in device manager and select properties. Should give some idea what is wrong.
Assuming it is a resource conflict, easiest thing to do would be to move the offending card to a different pci slot. Avoid the slot closest to the power connectors, even if you have to move another card around to do so. If that doesn't work, you should be able to change the allocation of resources to the pci bus in your bios setup. Too many variables there to give much detail. If you need help, provide info for your motherboard -- manufacturer, model, bios flavor and version. Also report what you see in the properties box for the nic.
Now to the rest. As marcs41 said, it is possible to set up a VPN server with only one NIC. I wouldn't, but you are welcome to if you must. I would probably pull the web and ftp servers over to the new card as well. If you are running a lot of web/ftp traffic, I would consider a third card.
To qualify that a bit, there are different reasons to separate the different kinds of traffic. First and foremost, you should never have public internet traffic hitting the same interface as your private network. It is somewhat of a security risk and it can hurt the throughput of your server on the local net. Since you are passing FTP/web traffic through your router to this server, it qualifies.
Your initial VPN connection qualifies for the same reason. Once the link is established, the security risk diminishes for the most part, but if your other public traffic is heavy, the VPN can hurt performance there. One or two VPN clients and light to medium FTP/web traffic should be fine on the same NIC.
Last item this post. You mention Access db . . . be aware that unless you have a really big pipe on both the VPN server and the VPN client side, Access will be really really really slow and unreliable. Maintaining code should not be too bad, it will take a while to load and save, and I would save a backup just in case the connection drops in the middle. Running a query or updating records is the real problem.
Keep in mind when deciding if you have enough bandwidth to do this, you are limited by the narrowest segment. If, for instance you are connecting by cable from your home, you probably have a 2.5M connection plus or minus. But, the rated speed is usually your downstream bandwidth, your upstream is only a fraction of that, probably 768K. Therfore, when you initially open the db, you will be limited by the upstream on the VPN server side, unless you have a more direct net connection, and when you save/close the db you will be limited by the upstream on the client side. If you really must consitently and reliably edit Access, consider some sort of terminal service.
Hope this helps, and hope I haven't rambled too much. Good luck!