Q: Has anyone else who uses AT&T as their carrier been told if you cannot access your voicemail through your iPhone that there is no way to check your voicemails? This is an issue since I had to send my phone in for repair. Thank you

Why can't you access yoru voicemail on your iPhone?

What happens?

-> http://www.att.com/esupport/article.jsp?sid=KB95761#fbid=hzkH8onZdN5

-> http://support.apple.com/kb/TS4430

You received incorrect information from AT&T.  You can indeed access your voicemail without your iPhone.

Call AT&T at (800) 331-0500 (assuming you're in the U.S.).  This is a 24 hour a day, 7 day a week number.  Ask them how to access your voicemail.  Normally, you would just do this by dialing your number from another phone, typing "*" once your voicemail recording starts, and entering your password.  You don't know your password, so it's probably the last four digits of your phone number or perhaps the seven - or ten-digit phone number.  Let the AT&T person tell you.

Call AT&T and explain.  Have them email you a password, or some similar solution.