how can I'll use my xbox points

What points are you referring to?

It isn't connected to any other devices when I tried using it with my Xbox one. It was random, just stopped working with my Xbox on the 16th. I tried using my other controller to see if it was a matter of needing an update for either controller to no avail.

At this point I think I'll just refund and get a replacement as it is in warranty and the problem at this point is unsolvable no matter how many troubleshoot methods I do.

You have to make a purchase on the console. You can't use the balance to purchase gold, so that's why it won't work with that. If it's not enough to cover the total amount of an item, you can split a payment by using a credit card first and it will ask if
you want to use your remaining balance.

Well the lady at Xbox did suggest that I set up a new email account and access xbox live through that. However, I'd need to buy the original points again, although i'll be able to share game content etc.

I've set up my new account- registered at windows live. Do I have to repurchase xbox live membership or can i use my original? If so, how?

I like the point he brings up on how they give us the ability to plug in cable, yet offer a good amount of streaming services. And that's what I'll be doing, the HDMI in is for my 360.