You shouldn't need the parental controls changed to log onto Xbox Live. However, since you switched computers make sure that your Xbox is getting connection to the internet correctly. You can 'Test Connection' in the settings tab of the Xbox home screen.
If you are getting the internet connection correctly and logging in with your normal Gamertag, you should have no problems.
I am unable to connect to my network when i know its running fine, i believe it is the internet plug...
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I am unable to connect to my network when i know its running fine, i believe it is the internet plug in the xbox 360 consol that has the issue