Maybe you guys can help a tired soul here.

I have an osCommerce store in front of me here
www.lexracingusa.com. When you log it takes you to a secure page and then it says welcome name

but

On all the non-secure pages it says welcome guest!

As a consequence, you can log in (secure page) add items to a cart (unsecure page) but you can't check out because the items were added to a guest cart and not your own.

Any ideas as to what could cause this problem?

probably something to do with the fact that you're using cookies (either sessions or full) which are set to only be read when in a secure environment, so when the script tries to read the cookie in the non-secure pages, it can't, thus decides that this person obviously isn't logged in/signed up