Start with the simplest first...make sure you have mobile data and wireless enabled in your phone. If the inability to download started after an upgrade or installation of any applications, try removing them. Remove the battery, reinsert, beboot. If all else fails, try a factory reset.
Check that you didn't turn on DATA SAVER : Menu / Settings / Battery & Data Manager / Data Saver
Also, Menu / Settings / Battery & Data Delivery < do you have "DATA ENABLED" selected?
I had the same problem just last week. As Cody21 said, make sure your Data Saver is off. I had turned mine on thinking it would help with things running in the background. The only way I could upload or download was to connect to my home network. After turning off the Data Saver, it works just fine.