to Cable Forum, sorry it's not in better circumstances.
It does sound as though ntl have really messed this one up. I think you may have caught ntl at a really bad time because of all their speed upgrades on broadband has placed an excessive strain on their capabilities. However that is no excuse and inability to properly resolve your porblems in a reasonable timescale is appalling.
As you say free service for a month is fine, but not really a benefit if it still does not work.
I do suggest you put in a more forceful written complaint, perhaps to you ntl area manager. Phone CS faults again, and explain you need a resolution to this issue, and today, you've been waiting nearly a week. If necessary require the issue be escalated.
If you still need a straight through ethernet cable, any local computer shop will sell them. Most bb kits that were supplied for STBs had a long ethernet cable, a plug in USB adaptor that connected to one end of that cable, and a plug in crossove adaptor cable for the other end. Check that adaptor has been unplugged.