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I can't remember much other than a kid got an old laptop, maybe from his school, and wanted to play games on it but it's actually an alien laptop and connects him somehow to other aliens. I also remember an alien government or something chasing after the kid. It was a book aimed towards children, I read it in the mid 2000s when I was about 13. I also remember there being some kind of interactive website/game thing that was attached to it, but I can't find anything about it because I just can't remember enough and google has failed me.

This is almost certainly the Outernet series. I also read it in the early/mid 2000s. Here's an excerpt from Wikipedia's description of the first book (emphasis mine); I include also mentions of some other key characters and story elements (Loaf, Merle, Bitz, Googie, Help) in case they ring bells for you:

On Jack Armstrong's birthday, he received a laptop computer from his parents, British residents working on a US military base. They have been having financial problems so he is grateful for the gift. He explores it with his friend Lothar Gelt (nicknamed Loaf) and their acquaintance Merle Stone, where they discover it is a piece of alien technology. Once turned on, it enables them to communicate with a stray dog around the base named "Bitz", who tells them he is actually code-named Sirius (a pun on the "Dog Star" of the same name). He and Merle's apparent cat (named Googie, code-name Vega), are both members of the "Friends", a group dedicated to resistance of The Tyrant, who leads the FOEs (Forces of Evil). Specifically, they are shape-shifters who have become permanently trapped in these Earth creature forms. They explain how The Tyrant has captured all of the servers in the Galaxy except for the one that Sirius and his companion Janus brought to Earth and disguised as the computer. The Server's "Help" program, which activates whenever its name is said, is sardonic and fails to live up to its name. Jack receives further proof of the truth of these odd revelations when he is teleported (called t-mailed) to meet Janus on another planet (teleportation through "N-Space" enables the characters to travel faster-than-light).

Throughout the series, Jack and the other main characters travel around the Galaxy being pursued by the FOEs, trying to stay alive and ultimately to bring down the Tyrant and the FOEs. Time travel gets involved in book 4 or 5, and there are some surprising twists at the end.

Wikipedia also mentions:

The book series asked the readers to access an internet site named www.go2outer.net. That site is no longer active and, in fact, is for sale.

I don't remember the details, but there was some fun interactive stuff you could do on that site, playing as if you were a member of the Friends working against the FOEs.