Yeah you definately shouldn't need a serial number for Creative Cloud, just your Adobe ID. I'll have some things checked on your account from our side.
Sorry to hear about your difficulties.
Based on what I'm seeing it looks like your Creative Cloud Membership was never able to activate and that your trial simply ran out. I see that you contacted our support on 7/10. I would recommend following up with them again. Some setting or software on your computer might to be preventing you from activating and your credit card being charged.
Here is the info to contact them
Monday-Friday, 5am-7pm PST