Is the WIC plug and play or are there commands that I need to run? The router is not showing the interfaces. I tried using the sh diag and it didn't show anything.
You're running IOS 11, but you need one of these (or higher) for the nm-2fe2w card to work...
If you have enough DRAM / Flash, I would go with the latest 12.2 for the Cisco3620... that's 12.2(26c)GD...
c3620-d-mz.122-26c.bin image will fit on 32M DRAM and 8M flash... avoid 12.2T if possible. As we discussed in comments, load it on a PCMCIA with another 3600 and sneakernet.