When I log onto icloud from my laptop, it does not appear to have any of my contacts.

I am attempting to back up my phone as my ability to connect to the internet with my data connection is not working. They have told me I need to reset my phone to get my data portion working. I can still text and make calls, connect on wifi, but can not connect to the internet via my cell/data. I don't want to reset my phone if I don't have to.
Erika...