The unauthorized error message can sometimes be due to a completely different problem than permissions. Anyway, try this for checking the connection:
start up the command prompt on both machines.
On computer1 type:
ipconfig /all
There yuo get a list of the settings for the nic. Look at the ip-address assigned.
On computer2 type:
ping [ip-address] and swap [ip-address] for the ip-address of computer1.
If you get a response you at least have a working connection to the other computer. So then try checking the things already suggested like:
workgroup(should be the same on both)
file and printer sharing for microsoft networks(this one i forget from time to time even though i think it's default for it to be installed

).
Then open up a browser windows(for example windows explorer) and in the adderss field type in "//" (without the "") and then the computername of the other computer. you should then get a list of the shared folders, which should be the shared documents folder at least. For example my computer is named "Lazio" then I would write
\\lazio
If it still doesn't work tell us and I'll try to write down more things to check. Hoem networks are sometimes harder to setup than office networks, but maybe that's just me....