OP, you need to figure out a way to get your microphone up next to your face. The Snowball is a condenser and without being close to it, your voice just isn't hitting it with enough power to drown out the majority of the noise in the room. This is one of the primary problems with the Snowball because the microphone mount to put it on a stand is proprietary and expensive. If you can get that mic 5-6 inches from your cheek (45 degrees to either side so you're talking past it and not into it) you will notice a huge decrease in background noise.
From there, the minor noise that is left can be dealt with by Audacity noise removal. But if you're just going to leave the mic down on the coffee table in front of you, then you will be plagued with noise for a long time. Getting it closer to you will also remove the room echo that you have.
You can also put a rug or sheet over the computer temporarily to dull the fan noise but I wouldn't recommend that for long as it kills the airflow which is what keeps your computer from overheating.
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This issue has nothing to do with the quality of the microphone. It has to do with the type of microphone. There are plenty of sensitive mics that are extremely expensive. I use the Shure SM7B ($400) and if I have the gain up on my mixing board, it can hear a door opening up two floors above me.
This one is all about positioning and settings.
, damm its a 360 
