What said your connection was fine? Again, if your modem lights are going in and out then its either a modem or line issue.
Go here and do a speedtest and give us the results along with what speed you are paying for.
www.speedtest.net
PING: 1634 ms
Downloadspeed: 0.08 Mbps (this used to be 280-330 Mbps)
Uploadspeed: 0.14 Mbps
I can't say what speed I'm paying for, sorry. Where can I find that?