Since all the telephone companies were deregulated, the practice is to have a demarcation point (which I'm really surprised no one else has mentioned yet). Most homes built within the last 20 years or so will have one, which will be a box or jack (often marked "DEMARC") marking the change in responsibility between their network and your in-house wiring.
Presumably, being a DIY site, you'd like to avoid being charged $85+ for something you can fix yourself, so there are really two steps to take:
- Isolate the problem to either their equipment or something before the demarc, or your in-house wiring
- If after demarc, isolate the problem to a particular jack
Connect your modem to the demarc
Best thing to do is disconnect all your house wiring from the demarc (usually it plugs in) and connect your modem to it, then run speed tests or whatever else. You may also want to try a different cable just to eliminate that.
Plug your PC/laptop directly into the modem if you can, to eliminate router/wireless, or at least plug your PC directly into to the router.
If you still have the problem, then it's either a problem with the wiring before the demarc, or your modem (both of which are the company's responsibility), or something on your PC/router (which they'll charge you for, and off-topic for this site).
If your Demarc is outside, you'll have to be a bit more creative, but at least you can just have one jack connected at a time (see the in-house wiring bit below).
Create a Demarc
If you have a wire that comes in and is directly hardwired to the house wiring, I'd suggest cutting it off and putting a demarc jack in (like the second picture).
Use a second jack to hardwire the rest of your house to, then a regular station cord to patch between the two. This also lets you disconnect the patch cable in order to do work on in-house wiring without worrying about shorting anything out or shocking yourself.
In-house wiring
If it's working at the demarc, the you've isolated the problem to the house. This could be much harder to diagnose.
If you have the same number of wires as jacks, then you have centralized wiring. If not, you probably have a harder-to-diagnose mess.
The new way: Star topology
If you're lucky, each jack will have its own cord coming back to a central location, where they'll probably all be connected together. Detach all but the one you're using (this may take some trial and error) and try the modem there. If it works, then there's a fault in another wire and you can isolate that one-by-one, or just leave it disconnected. Repeat for another jack or two in the house.
The old way: Branching/Daisy-chaining
Technically for phones to work, the ring and tip wires just need to be connected in parallel. Many times the jacks are all or partially daisy-chained, or even worse, there are junction points hidden in the walls, in whatever way works to make the shortest wiring possible. One of the problems with this is if there's a fault, it's extremely hard to find.
You pretty much have to follow the same steps -- trying to isolate lines -- but you'll have to disconnect wiring in the boxes around the house (and hope there are no hidden junctions). It may be simpler to just run a new jack and new wiring from the demarc to the spot you need, and leave everything else disconnected.
Does anyone have an idea why on the same circuit 4 boxes have 240V and 3 boxes have only 120V?
It may be there is a loose/corroded/burned connection in the 4th or 5th circuit box.
It may be you are using a voltage detector that has LED indicators for specific voltages, and does not make an exact measurement.
I would turn off the circuit breaker for that circuit, lock it out (to prevent other people turning it on), verify that nothing is live, verify again, then check resistance from live on 4th socket to live on 5th socket using a good quality Cat-II or better meter.
Best Answer
Have you tested that the problematic jacks are actually wired to your house's phone system? Just take a land phone and plug it in - do you get dial tone?
If you're not getting a dial tone, these jacks are disconnected. Perhaps they were wired to a second line that is no longer active, or simply cut during some other project. To fix that, you'd need to reattach them, tracing the cables and re-connecting them to your main phone service lines.
If the jacks work for phone but not DSL, there may be a DSL filter installed between your main phone line and those jacks. These can be wired inline somewhere, or even built into the phone jacks themselves. Check the jacks first - do they have DSL-related labels? Can you remove the cover and look inside to see if a filter is there? Perhaps they are connected to another jack that has a DSL filter.
If the filter is wired in elsewhere, you would need to trace the wires from jack to your main phone service termination point to confirm.
EDIT: if you don't have active phone service, you probably won't be able to test with the phone/dial tone method. Instead, you can try a tone & probe kit or test voltage on the lines to see if they're connected to your house phone system. Although I'd still try a land-phone test as it's entirely possible you are supplied with a dial tone even if you can't make or receive calls.