Phone not connecting to the internet?

So my phone WILL connect when I m on an actual internet connection (sorry I m not techy, and don t know what it s called but one in a house or building that shows up under wifi, like my house one). However when I m not connected to a wifi (is it called roaming? If not, ignore that, but anyway) it will not connect. I constently have either H, H* or 4G but it will not connect to the internet. I have a samsung galaxy S4 mini. I have also noticed that under the wifi letter (the h, h* ect symbol) there are two arrows. I have no idea if this matters but only one ever seems to be filled in.
Also, I think the 4G might be a lie, because i have never known anyone to get 4G around where i live, we can t even get 3G.

Any ideas for what is causing this, and solutions? Also, sorry if I sound like I haven t got a clue what I m talking about. The reason is, simply, I don t have a clue what I m talking about! :)
Thank you!

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