Windows based hosting with a SQL Server database for $3/mo can be a bit tough. You may have to raise your budget a little, especially if you're looking for quality service.
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You may want to try m6.net, the pricing is near your budget and they support ASP Net 3.5, have been using it for some of my personal domains. Responses aren't that fast about a day or two and the phone never seemed to be able to reach anyone. Other than that quite decent performance for such prices.