I will do my best to help you send a fax from your PC but this is a very rare issue so I hope I can help without buying any new hardware. It may come down to that however. I want to ask a few more questions so I can give the best advice.
1. The 8600 has three printers in this series. There is the 8600 (N911a), the 8600 Plus (N911g), or the 8600 Premium (N911n). Which one do you have just in case I need to send you any links specific to your unit?
2. Since you are receiving an error that the computer is disconnected, how is it connected (USB, wireless or Ethernet)?
3. When you say fax modem, can you provide a brand name and/or model number of it?
4. What type of fax service do you have? By that I mean do you have DSL, a designated fax line, or if this fax line is shared with a voice line, fOIP, etc? The more details about it the better.
I know DSL can interfere in a lot of ways so for now I suggest going into the fax settings on the front panel of the printer and turning fax speed to slow and Error Correction Mode (ECM) off. Do that for me, try sending a fax again, and if it fails, answer those questions for me please.