Can you use a normal nonprepaid ATT SIM card in a prepaid ATT GoPhone?

Yes.

I have used my AT&T Wireless account SIM card in several GoPhones since breaking my original A&T phone.

Yes you can but it is against the AT&T TOS (terms of service).

GoPhone (Prepaid) Terms of Service state the following:EQUIPMENT: Your Equipment must be compatible with, and not interfere with, our service, and must comply with all applicable laws, rules and regulations. We may periodically program your Equipment remotely with system settings for roaming service and other features that cannot be changed manually. Roaming service is the use of your Equipment outside our service area. Equipment purchased from AT&T or its authorized dealers is sold exclusively for use with AT&T GoPhone service. It may not function on other wireless networks. By purchasing this Equipment, you agree to activate and use it on GoPhone service.