Problems syncing MobileMe mail with an iPad 2
To help you in focusing your troubleshooting - here are the variables:


Your MobileMe account status
The network between the iPad and the MobileMe servers
The steps you take to configure it
on the iPad
The software on the iPad
The iPad hardware


You seem to have tried #3 again - so unless you have never successfully entered a MobileMe account into an iOS device and had it work, it's unlikely having someone else do the entering will help solve your problem.

To really rule out #4 - I would transfer all purchases and back up the device. Then I would rename the device to "test" and restore it. Once it's restored, I would not load a backup and set it up as a new device. Second thing after joining a network would be to try MobileMe setup. If it still fails you can rule out #4. Then you could restore your backup to get everything and the iPad name correct again.

You'll need to take your account to another device to rule out #5. This is unlikely since if the hardware is failing, everything should fail equally. There's no little chip inside the iPad that computes the sync data - it's all software for that.

Eliminating #2 should be easy and it's highly unlikely to be the cause - possible, but very unlikely.

Lastly, you will need to get help from Apple MobileMe support if you need someone with access to the servers to see if your account is having problems. I needed their help last year to realize that my iDisk was over quota and syncing having errors as part of that space was needed to store my data during a sync. MobileMe is an evolving thing and something that caused problems in the past might now be fixed and new things could be causing your account to not show other data to be synchronized.