Internet/computer troubles?

In the middle of October, I started experiencing internet/computer lag. (Don't know which it is.) I started having lag in Skype calls. I still get it to this day, it's like everything stops. I can't hear the person and tehy can't hear me. Then 4-10 seconds later, it comes back. And everything is fine for a few minutes then it does it again. It's really annoying. I also play Minecraft and everything freezes, all the players stop moving, everything, the sounds stop, and then 4-10 seconds later it comes back on, and everything is fine for a bit.

Can someone help me out here? It's been going on for awhile now, we've called our internet supporter and we upped the GB of internet space we have, and it still didn't help. It does not happen to my brother at all, which makes me think it's my laptop. I have a Toshiba, Satellite C875, 64-bit Operating System, x64-based processor, Windows 8, Intel Core i3-3236M CPU, 2.20Hz 2.20GHz. I have 5.88 GB RAM usable out of 6.00 GB of RAM.

Should I contact Toshiba, or should I bring this up to my internet supporter?
If you know how to fix this please help. Thanks so much! Have a great day.

Added (1). It's also very snowy and cold here. Almost 6 inches, could that be the problem? We started getting some snow/cold weather in October.

As much as I can tell from your story you don't have a problem with internet connection, what you have is a slow PC, not slow because it is weak but slow because it is somehow full. The best thing I can recommend is reinstalling your operating system. If you don't want to do that try other things. Clean the registry, unnecessary files. Anyway PC needs to be formatted ( reinstall the operating system you have got), if that is a big trouble for you then try these software that clear the registry and unnecessary files for you.
CCLeaner, free does whatever is necessary.
Uniblue power suit (includes speed up my PC and registry booster). This is not free but it can be found free from torrents easily.
Advanced system care

Takeoff all the software off you do not use any more.
restart your computer
or it may be the snow
go to my web site at http://anthonyscomputerhelp24641.weebly.com and go to my internet help page.

If some program run in background you can have this lag. To fix it do next.Go mStaret / Programs / Accessories / Run. Type msconfig.
Click OK. In new Window click tab Startup.Uncheck the programs that don't need to run on startup (don;t uncheck System programs).
Click Apply and OK. You will need to restart computer.