Sounds like interference.. aka- noise on the line. Those Compaq built-in modems really don't deal with it well. Bob, if you call your ISP they may be able to walk you through some setup stuff on the phone that will diagnose (and maybe fix) this better. In the meantime, common causes of sudden noise on the line include adding jacks or otherwise altering the house phone wiring, having a phone cord (PC to wall) that is very long (esp. if it's all tangled around other wires or around electric gear), adding a new phone to the line, or running your PC phone cord through one of those female/female adapters that let you plug two phone wires together. I had a wicked problem with this in an old house, turned out to be a staple punched through the wire by the installer. Problems like this can lie dormant for years, or creep up the first time you try it.
Try it on a different phone outlet in the house. If you can, try it on someone else's line. If it works in either of these situations, you may have narrowed your problem a little. I'm hesitant to tell you to get a new modem. Cheap or no, I hate seeing people spend money on stuff that only MIGHT fix the issue. Either way, the ISP can guide you through some stuff that will be more definitive than what some dude on a gun forum can cook up. if you end up needing to buy any computer components to fix this, shout on here before you hit Staples or whatever. My father (not real savvy) went in there to get a few $5 extension cables for various gadgets he has on his PC.. Should've run no more than $30. $100 later, I'm standing in Staples tearing some little bastard a new one for handing my dad the $25 USB extensions and all sorts of crap he didn't need. The manager seemed not to understand the problem. Great bunch.