It sounds like the speaker module could be damaged, or perhaps it has a bad solder connection. I would start by trying to resolder the connections for the speaker. If that is not successful, you'll have to explore replacing the speaker module. You'll find that the speaker is actually soldered to the dock connector/headphone jack/logic board assembly. Replacing it will require careful soldering and you'll have to locate the part. Currently, there is not a iFixit guide for replacing the speaker module, but [guide|11809|this guide] will get you in the neighborhood. Review the material before deciding if this is something that you want to tackle. You should be sure that you have the proper tools and feel comfortable with what will be required to perform this repair.
Good luck!
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