You can certainly give it a try, is the internet from timewarner do that on every device you have hooked up to that service? If not it could be just the one computer, also you may be able to request a new modem, or purchase a cable or ssl modem from the stir or online and that may resolve your issue.
Are you connecting wirelessly or with a cord?
Do you have a router or are you connecting directly to the modem?
I haven't had DSL since 2001, but I absolutely hated it. Been on cable ever since. Time Warner from 2001 until whenever Comcast bought them in this area. Comcast ever since. Nothing can even come close to touching them on speed. Though I'll switch to fios if they ever bring it here.
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