You can have already ruled out your computer because it works fine on dial up and your modem because you have two and neither works.
The next step is to verify the wiring you are responsible for is good. The equipment inside your apartment from the demarcation jack is your responsibility (or that of the landlord). Check out the
Bell support page about troubleshooting this and make sure everything is good.
From the description it sounds like there is something wrong with your loop. If the problem
is with the DSL equipment "behind the wall" (from the demarcation jack to the DSLAM) switching providers will not change that. All that equipment belongs to Bell and the resellers just, well, resell access to it. Switching to Cable would "fix" it; that is assuming the cable equipment behind the walls in your apartment is good. I know some people who lived in large apartment buildings and DSL was a constant problem for them because the buildings were very poorly wired.
Bell technicians have special tools to test the quality of the DSL signal at your jack. I would contact your reseller and demand they send out a tech to test the line and fix the loop. You will have to go through their troubleshooting process of testing your PC and modem first. They will not want to send someone because they do not actually have technicians to send; they have to contact Bell and get Bell to send the technician and this cost them money. If they are not willing to help you then you should probably switch to another provider and find one with a good reputation for customer service.