[SyCo]

Unlikely to be you modem, but possibly, they usually work or not. what the model number (the exact one on the bottom)

A couple of IT classic steps first.
Have you tried turning it off (wait 30 mins) turn it on.
Are you sure its plugged in correctly and all the cables are undamaged.

It could be a few things. As you have multiple computers then I presume you have a router (both PCs can connect at the same time). Is the moden also the router? if it's 2 boxes connect the network cable signal directly into the PC and see how it does.

Most routers now are also wireless. So even if you computers are not using the wireless signal it might still be out there for someone to steal. It's possible your neighbors kid is downloading using your bandwidth. This can cripple but not kill an internet connection. If you're connecting slowly and sometimes this would be the first thing to fix. Log into your router to add wpa2 security and change your router's default passwords. You can usually get a list of connected clients. It's possible your neighbor has accidentally connected (really accidentally), you will see their computer name which might give you a clue.

If it's still crap it might be a network issue outside your control. Your street might be maxed out, the signal strength might be reduced because of distance. etc. Either way a call to Verizon is the next step and see what they have to say. I had sub contractors block my internet for technical reasons and not tell me. Only after an technician came out they found the block and fixed the problem.

If the problem has arisen recently and it used to work fine then it's most likely a verizon issue or someone is wardriving (stealing wireless).