Vikky - you may be able to read this reply and see what you're typing, depending on your screen font size. I set my to the smallest setting (with the monitor in 1280 x 1024 resolution mode), and I can scroll down enough to see your reply while typing. (It's down below the reply area that I'm typing in now.)
Anyway - if I'm following you correctly, your fax/scanner is connected to your computer, probably on a USB port or maybe by a serial cable (9 pins). It used the old 2nd phone line that you had turned off when you had DSL installed. However, was the phone line connected to your computer or to the fax/scanner? I suspect it was connected to the modem card in the computer, and that's how the fax could make and receive calls. The software told the fax what to do while controlling the modem card. And, you've now switched from the "old" modem (56KB type) to the "new" DSL modem.
So, since that new modem is looking only for the DSL data (high freq) signal and is ignoring the voice (low freq) signal, that's why you're not getting a dial tone. You're always connected to the internet, so your computer sees the data and doesn't see incoming calls. Also, without the filter you described before, your phone's not able to see the voice (low freq) signal, so no dial tone is present.
You mentioned the dual connector (splitter?) and the test you did. When you had the DSL modem plugged in on one side, and the phone plugged in on the other side, did you see if the computer was still connected to the internet? If the DSL modem still works (you can hit the internet) and the phone doesn't, then it sounds like all you'd need is one of the filters you described before along with your old 56KB modem card. You'd place the filter between the splitter and the modem card, which would now only serve the fax machine. Hopefully, your DSL modem and your 56KB modem can peacefully co-exist in your computer. If not, you'd need someone on-site that would be able to possibly hook up other hardware (e.g., an external 56KB modem box) and make the proper connections so everything would run.
At home, I have the DirecWay 2-way satellite system and its modems are external. They connect to my computer on a USB port. My old 56KB modem circuit card is still in the computer, and it functions fine - the two systems don't interfere. I can dial out on the 56KB modem if I choose to. I did have to set up my browser to "not dial a connection" so it'd ignore the 56KB modem and use the DirecWay modems. That's why I'm thinking you can have both your DSL modem and your old 56KB modem both hooked up and make teh system work - once you put one of the filters on the line connected to your 56KB modem.
Again, I'm not DSL-literate, and what I'm describing may not easily work without some software reloading and tweaking. Your DSL installer should know how to make the fax/scanner connect and work with the voice (low freq) portion of the line while allowing the computer to use the data (high freq) portion of the line.
I hope this wasn't too confusing...and I hope it helps you reach a solution soon! Regards! Jim D/Heathsville, VA