Access Denied on one computer, but not another using same user
Are you sure the two computers access the same address? It's a common mistake to have both www.yourdomain.org and yourdomain.org (without the www) that display the same pages. 

Unfortunately, connecting to one doesn't automatically connect to the other, even if they look exactly the same. It's the same with the protocol, so login on http:://yourdomain.org doesn't mean you are authenticated on https://yourdomain.org.

Check what is the main domain name and protocol, the one put into civicrm.settings.php, it must me the "official" one and it's where you have to do and login to work properly. That's probably what was done on the computer that works but you are logged to the "wrong" domain on the second one.

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