Did you add permissions for your Xbox 360 user account on the Media Center PC?
Right Click on the external drive you're sharing, and go to properties.
Next click on Sharing, Advanced Sharing, then tick the Share this Folder box(If its not already). After that click on the permissions button, and add Everyone, and the username for your Xbox 360 (Mine is Mcx1-"Username") [See bottom of post] Yours may vary though. You want to make sure the Everyone and Mcx1-Username both have "Allow" checked next to the "Full Control" row. Do this for both of them. Then click apply and ok.
After that you want to click on the Security tab on the properties window. Do the same with adding both Everyone, and the Mcx1-Username, and checking "Allow" next to the "Full Control" row. Click apply and ok. Another windows (command type window) will pop up and start showing various text. It's just changing the permissions, nothing to worry about.
After that you should be fine. See if it works now.
Windows 7 might have this issue as well.
***To find Everyone and Xbox 360 Username in Permissions, click on the "Permissions" button (The usernames, computers, etc... will be listed here), then click the "Add" button, then the "Advanced" button, and then the "Find Now" button. A list of all of the usernames or administrator names will appear. Do this for both "Everyone", and Mcx1-Username, and you'll be good. Make sure the Allow box in the Full Control row is checked (All remaining boxes will check when the Full Control Row is checked)
***To find Everyone and Xbox 360 Username in Security, click on the Security tab on the main Properties window for the drive your sharing. Now click on the "Edit" button (Again, the usernames, or computers your PC is giving permission to will be in this list). Next click "Add", then "Advanced", and then "Find Now" (Similar to permissions). Make sure you add both "Everyone", and the Xbox 360's username. Be sure and click on the "Apply" box in the "Full Control" row for both of them.