First, look at your fax cord. The fax doesn't likely require six pins so find a 4 wire jack. My understanding is the phone runs on only two wires and the second pair is for a second phone line or a jack accomadting a two line phone.
Since your house does not require two pairs in the second floor jack, it sounds like the second floor jack you mentioned is likely in the middle of a run which then continues to another room. At the end of that run you will likely find only one complete set of coloured wires.
In many older homes phone jacks were often on the first floor and basement only. If you have two different clours of wiring someone has upgraded along the way.
As JB said you need to find the demarcation point (entry) in the basement and determine the colors there. Wires coming in, if they are old will likely be yellow, red, green, black. Find the first junction in that line and you can likely find where the second floor lines connect and what their pattern is or go to the main level and look at how that jack is wired.
Simpley duplicate the pattern from that point to your new 4 wire jack and you should be fine.
For simplicity, match the positioning of wires to theh pattern used on the second floor as it has the new striped wiring. This wiring is referred to as twisted pair and is low voltage.
If you are really stumped you can just strip the ends and flip the wires teminal to terminal before installing the jack intil you get a dial tone and no static.
Also when stripping this wire breaks easily, leave some slack. I try to strip it with my thumbnail so as not to break the copper inside.
Call us and let us know how you make out