would a AT&T, Cingular, Fido, Rogers Wireless, phone work on a T-mobile sim card?

No..If it's unlocked means, you can use the tmobile network.
Otherwise you have to unlock it and use the tmobile sim. This unlocking can be done through codes.If you need , get it from Unlock-free.com .It's free service.If your mobile model is listed here, you can unlock your mobile easily.
 
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