That sounds to me like the Headphone jack assembly (includes top button, volume, silent buttons) has been either dislodged or damaged due to the drop. Two ways to fix this. If you are confident with taking apart your iPhone then you can try to re lodge the top button (this means unscrewing it, re sitting it and hoping for the best). While you do this you can also visually see if there is any further damage and if anything has become loose/is missing. You will find that the button itself will most likely be fine, it will be the connection below it which will be the problem.
Below are two links, the first in how to install the top button, the second on what to buy to replace it.
iPhone 3G Power Button Replacement
iPhone 3G/3GS Headphone Jack Assembly
Now from experience the headphone jack assembly is very 'fidly' to install and takes a fair bit of patience, time and experience. If you are not confident with this then i would recommend to buy this.
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This includes the new headphone jack assembly pre-installed for your convenience. Just re install your logic board and you are good to go.
Second option is to take your phone to an iPhone repair shop and let them do all of the hard work for you at a cost. But if you are not familiar with the internals of an iPhone i would highly recommend taking it to someone who knows that they are doing. I have seen way too many phones come in with the customers trying to fix it themselves and end up breaking the entire phone.
Hope this helps!