Buying a new computer can be exciting. Finally, you're done with that old hunk of junk that served you so well in the beginning before turning into a slow, useless paperweight. But what's this? Your brand new computer is scarcely faster than the one it is replacing. While this is a rare situation, it does come up occasionally and there are some reasons why it might be true for you.
Regardless of a new computer's high-end specs, it can't make your Internet connection any faster. If you haven't upgraded to high speed internet, your brand new computer won't be able to do much with your old 56k connection. Many areas--particularly in close knit communities such as apartments and dorms--share even broadband Internet access to the point where it's difficult to get good speeds. It's frustrating, but it's not your computer's fault.
Somewhat related to the first point, if you're dialing in to a home network your new computer may have networking hardware that is incompatible with the modem and router in the house. This incompatibility, such as an N-series router connecting to a G-series adapter, may work, but it will produce slower Internet speeds and intermittent service.
Just because a computer is new doesn't mean it's ready for today's computing world. Computers with low specs, such as weak processing power and tiny amounts of random access memory (RAM), are sold to the budget market because they are affordable and users aren't told the full truth about their performance capabilities. While these lower-end computers may run a word processing program and solitaire without incident, gaming and watching streaming video could pose a problem.
Higher-end computers are usually bare bones affairs, allowing the user to fill up the program space with whatever applications they want to run. Budget computers, however, are another story. The ones that come with better specs but an ultra low price tag are usually overrun with programs that you don't want or need. The computer includes those programs because the manufacturers subsidize the cost of the machine. Getting rid of some of those programs could speed performance.
A new computer that runs really slow could simply be a lemon. Before wasting a lot of time trying to come up with quick fixes or searching for problems, it might be worth it to simply return the computer to the store and try another one. Computers don't last forever, but they should serve you well for at least five years. A computer that starts slow is only going to get worse.