Well if you have run out of room, you won't even be able to access the internet eventually as when you visit any site, it puts data and files on the computer. Which takes up room.
Most computers, even when they are new, have quite a lot of space. And it isn't that they have less than the specs say, but that the software they have installed, including the OS, take up some of that space.
If you want to keep using that laptop to do anything, including accessing the internet, you will need to clear off space. If you don't want to delete files, you can simply ZIP up the ones you want, but don't use all the time. That will free up a little space.
Otherwise you would have to consider some form of external drive.