The phone line is correctly connected to the all-in-one but...

try pulling the cartridges out, and then reinstalling them. make sure to go into the printer settings, and do a printer cartridge cleaning after.

I had same Problem ones just reinstoll your printer driver, gave it a try

I would check and verify you have dial tone on the phone line and its plugged in correctly, possibly replace the phone wire from wall to fax if necessary.

Only if you have fax software on your computer and scan an image to the computer to fax, otherwise you need a really long phone cable you can buy at Radio Shack or Best Buy.

Have you checked the online support guides to make sure your fax is connected properly. There is a lot to work through, but you should be able to test your setup and see if you can send faxes but not receive them. See links here, here, and here. Treat the credit card machine as if it were a telephone answering device or another phone on the line.

I hope this information allows you to resolve this issue. If you need further assistance, please post back with a comment to this thread.
If I've managed to answer your question or solve a problem, please take just a moment to rate this post....thanks!

You need to install the software and driver for the version of windows that is on the new computer. 
Link to you model printer/scanner below:
http://h10025.www1.hp.com/ewfrf/wc/softwareCategory?lc=en&dlc=en&cc=us&product=1119598〈=en&

Make sure your that the printer is connected to the computer in a working USB port. Also make sure you have the correct drivers installed on the computer to be able to print using this printers.

Here is a link to your printer drivers:
http://h10025.www1.hp.com/ewfrf/wc/softwareCategory?product=1119598&lc=en&cc=us&dlc=en&lang=en&cc=us&submit=Go

After you click the link, you will have to choose your current operating system. If this doesn't help, please let me know and I will further pursue a solution for you.

The 6310 takes a #95 tri-color cartridge. #901 is for Officejet 4500 and 4600 series printers.

1-are you sure it is in the correct jack? there are two in the back of the printer
2-when you did the install it should have done a fax line check

perform the steps given in the below webpage.

http://h10025.www1.hp.com/ewfrf/wc/genericDocument?docname=bpu01832&cc=us&lc=en&dlc=en