Can a wirelessly connected computer share its internet connection with a computer next to it using a cable?

Yes I have done it before in Windows XP years ago, you need a crossover cable for direct connection or a small switch if you use a straight through cable. Then, on the PC with a wireless, open the Network Connections folder, highlight the two adapters, right click on them and from the pop menu select bridge connection. All that's left if getting the ip addresses right, if you have a dhcp server the other PC will automatically get the IP address.