Depending on the exact type of DC motor in the treadmill it may be a very large RF noise source.
Brush tpyer DC motors make electrical noise from DC to daylight (the arcs on the brushes).
A less than perfectly installed phone line is an easy victim for this type of noise.

Run a length of category 5 cable from a good quality phone jack right to the demarcation point (on the outside of your house). Use that jack only for the dsl modem. Add a dsl filter at the demarc point for the phones, disconnecting any unused pairs. That should improve matters.

Also get a filtered plugstrip (not just a surge strip) for the dsl modem. APC makes some decent ones. Warning - you won't get a good one for $10.

As Brickeye said it could RF induced. To check plug a resistive load, such as a lamp, into the receptacle to see if you still have the problem. If so, then it sounds like a different issue. I guess it is possible there may be a nail going through the say the neutral & one of the twisted wire pairs(keep in mind it might just slightly be nicked & when the treadmill runs the vibration makes the two make connections). Check the voltages on the phone wires while the treadmill is running.

You may want to do another test as well. Plug a hair dryer into the receptacle & see if you have the same problem. This is an inductive load as well & will generate RF noise but without the vibration. This is a long shot but easy to check.

Also, plug the treadmill into another receptacle on the same circuit to see if the problem continues. And then plug it into a receptacle on a different circuit. And to continue this debug process plug the DSL modem into a different phone line jack & test it, then a different receptacle but same phone line jack & test it, then a different phone line jack & receptacle & test it. This will help determine if the problem is "unclean" power going to the modem or if the phone line is having noise coupled onto it.

Are you using the same duplex receptacle to power the treadmill & DSL modem? Are they on the same circuit even if not on the same duplex receptacle? How close is the receptacle to the phone jack?

As Brickeye points out, your problem is most likely RF being generated by the treadmill. Your telephone line is working as an antenna, and causing your problems. The solution is to isolate your phone line as much as possible from the power line feeding the treadmill. As also suggested above, these problems can be reduced by using CAT5 or better cable for the telephone. No reason to give up your DSL.

I am curious as to what you determined the problem was or has it not been determined yet?