I have a new multi-function printer and FiOS Internet, Phone and TV. My old analog phones work just fine and get a dial tone through all the phone jacks, but the fax doesn't recognize the dial tone. I've read about micro-filter and splitting devices for DSL connections; will they help with my problem?
No, a DSL filter will not help with your problem. Do you have dial tone when you plug a phone in to the same jack using the same line cord? If no then the fax is not built to tight specifications and will not work.
On your vioce phones, do you get a dial tone the exact second you pick up the phone, or is there a delay, like a incoming voicemail msg that needs to be listened to? I'm willing to bet that your phone system tells you you have unheard voicemail messages by adding a delay before voicemail, and that will affect your fax machine. Clear your voicemail and try again.