In the US it was common to ground phone lines to the incoming water line. Water lines were iron. Mine is still grounded that way.
If lightning hits the pole that carries electric, cable and phone, even if the ground wire on the pole fails, there is still a path to ground OUTSIDE the building.
ADSL (residential dsl) is the same two Plain Old Telephone Sevice (POTS) red and green wires, but with the power jacked up to allow higher transmission speeds. Electronic noise kills adsl pretty quick. There was a jerk in my neighborhood who used to fire up a pirate radio station on the weekends and take phone requests. I lost dsl every Saturday for a long time, before complaining loudly to a couple of Bell techs about it.
His music was much better than the "Clear Channel Communications" garbage. BUT, I pay extra for dsl, so I expect to use it.
Anything that connects to the phone lines can inject enough noise to break your connection (answering machine, satellite dish with dial up for pay channels, fax machines, etc.)
Your inverter is probably mod sine wave. Which is really a nasty square wave with voltage peaks that do not match the mains. A high power mod sine inverter is radiating 60Hz square wave noise, so it needs to be grounded away from tv's, radios and your phone. The ringer on a phone uses 30Hz at about 90vac, so 60 cycle hum will mess up your connection.
Find a patch of ground somewhere (preferrably that stays wet most of the time) and pound a galvanized rod (not rebar) 3 feet deep at least. Get some supply wire rated for direct burial and connect your inverter to the buried rod.
