The kids next door have hacked into our modem/computer!

Help! I live in a duplex, basically a house subdivide into 2 separate apartments. We were informed by a neighbor that the kids living in the apartment next door have somehow managed to either Piggy back or hack into our Modem. Our IPS is a company named Time Warner & we have a internet cable connection. Both us and the kids next door have the same IPS. The problems we have: The computer will suddenly freeze. our connection will slow as to it takes anywhere from 45 seconds to 2 minutes for the page to load. We have had our passwords changed on our e-mail account's among other things. Before we knew the problem was originating from next door i brought the computer in to have it checked for viruses, malware, any technical problems & we were told the computer was fine. Thank you for reading our thread, any advice/help would be greatly appreciated.