Just to be sure the different SSIDs are not causing the problem, have you tried changing the SSID on one of the devices so that they are the same?
I've never used the range extender, so forgive me if I'm shooting in the dark here. Is there any kind of firewall built into the range extender that would need to be configured to allow file and printer sharing? Can you get internet connectivity from upstairs using the range extender (assuming that you are sharing an internet connection through the router)? Do you have MAC address filtering enabled on the router, and if so, have you entered the MAC address of the range extender in the table of allowed MAC addresses on the router? Are all WEP or WPA encryption settings conformable on the range extender and the router? Can you ping the router's IP address from upstairs when connection through the range extender?
Please explain what you mean by the following:
"Yes I can get internet service through the range extender upstairs, but not through the router itself"
Does the router downstairs connect to the internet? If so, then if you can connect to the internet from upstairs through the range extender, then aren't you also connecting to the internet through the router? Can you connect to the internet through the router downstairs? These are critical questions. If you can connect to the internet through the range extender, then it says that the range extender is working and eliminates some troubleshooting steps.
If you don't know what MAC address filtering is and you haven't set any security options on either the range extender or the router, then I doubt that MAC address filtering is the problem. A MAC address is the physical address of a networking device. All network cards, routers, broadband modems, etc. have a MAC address. MAC address filtering is a security measure wherein you enter the MAC addresses in a table in the router set up of all devices that will be allowed to connect through the router. If a device tries to connect, but its MAC address has not been entered into the table of allowable MAC addresses, then that device is not allowed access.