Favorites in IE8 do not work after being copied over from my old profile.

Try taking ownership, and Full Control over the new favorites folder, in case permissions were hosed. Maybe .url file associations are also broken?

Do they work outside of the favorites folder as well?

This is a problem in IE.
There is a Hot Fix released for this for XP and Vista.
Please use the following link to get the hot fix.
http://support.microsoft.com/hotfix/KBHotfix.aspx?kbnum=936881&kbln=en-us

Even though the Hot fix says IE7 its exactly the same issue IE8 and works fine.

To enable this hotfix after installation, follow these steps:
Click Start, click Run, type regedit, and then press ENTER.
Locate and then click the following registry subkey:
HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Internet Explorer\Main\FeatureControl
On the Edit menu, point to New, and then click Key.
Type the following subkey name, and then press ENTER:
FEATURE_URLFILE_CACHEFLUSH_KB936881
On the Edit menu, point to New, and then click DWORD Value.
Type iexplore.exe, and then press ENTER.
On the Edit menu, click Modify.
Type 1, and then click OK.

To disable the hotfix, type 0, and then click OK.
Exit Registry Editor.

Javed, it will not let me create a key. Error say cannot create key: Error writing to registry.

The old profile no longer exists.

I do have full control of the folder. They do not work anywhere.

I did notice that a shortcut that is on my desktop that works, has more options in its properties than the shortcut favorites that don't work. There is only a general tab for the shortcuts that don't work and the one that does work has a general tab, web document tab, and a security tab.

I also got an error code 40 when I tried unzipping the hotfix.

I had to copy the new profiles favorites back to the old one and then select them all from the old profile and move them to a new folder I created on the C drive. Then I just moved them from the C drive to the Favorites profile of the new profile. I was signed in as the new profile.