Would by old Cingular cellphone work with my tmobile sim card?

No you can't use your t-mobile sim in the old phone until you unlock it from cingular network provider .You can easily unlock your phone through online providers like TheUnlockArena.com here they are rendering network unlock code for all mobile models at reliable cost .You first check that whether the code is available for your mobile model ,country and network provider .If yes then pay for it and unlock your phone then freely use it with any GSM sim ...