After checking all telephone extension sockets and wiring, everything seems fine on that front. However, the line has become very noisy now, too much to even make calls or receive a dial tone. Any further clues as to what might be causing this? I feel like it is most likely a line fault at this point.

Certainly appears to be a line fault when noise on the line. Report a voice fault to your supplier, ignore the ADSL fault at this time as it seems more that likely sorting out you line will rectify this.

A lot of permanent noise is a good thing in many ways in helping trace a fault. I had similar symptoms to yours but only on an intermittent basis...that can become a nightmare as often engineers are trying to fix a fault that is not there.