Cat6 Ethernet connections
The eight wires in the cable are set up as four twisted pairs, as you've stated. Generally the pair colors are matched with solid and stripes wires of the same color; e.g. Blue and White-blue (striped or dotted), Orange and White-orange, etc.

Even if your cable doesn't include the striped markings, the wire pairing is critical. When building your cables, make sure that you use the correct white wire in any specific location. You can determine which is correct by noting which colored wire it is twisted with.

If you are already doing this, the next step would be to post close-up pictures of your cable and connectors, and we'll go on from there. You can edit the pictures into your original post by clicking the "edit" link directly under your question.