You don't mention what operating system, ISP and modem model you're using.
However, the two lights that you normally should have are ADSL and USB, ADSL tells you the connection to the exchange is ok or not, USB tells you the connection to the PC is ok or not.
ADSL will not light up if USB is not lit because the modem driver needs to be active before anything happens.
When you first switch on your computer there will be a delay while the modem establishes a connection with the exchange - on freeserve for instance I noticed it can take up to 45 seconds or thereabouts.
If your connection is ok but the lights are not showing it is possible that your modem is partially broken or, if you are using a USB hub, that it is not getting power to it from the PC (some type of USB equipment need to be connected to the motheroboard direct).
Let us have more info and we'll from there.
Cheers
Charles