Probably a noisy phone line on your end, or a bad modem or other problem at your ISP. I have dial-up and had this problem sometimes, and I could hear static when I picked up a phone on the same line. This happened for a while after rainy spells, so probably water in the cable. There were also vines growing around and into the junction box on the pole. About like this:
Finally I experienced a close lightning strike that caused more visible damage, and the Telco replaced the line. The arc apparently traveled down a large sycamore tree until it reached a power line, where it arced into the neutral, and causing a fireball that broke the window and got into the nearby phone line. I was working on my computer about 50 feet away, and I could smell ozone after the flash-bang.
Paul