Not a job for the faint of heart, I think, but if you do some googling you might find some replacements for this, and some may come with instructions for how to install them. The job usually requires considerable disassembly and delicate work, but it's done with some frequency.
If you don't think you're up to the job the only real alternative is to find a camera repair person or place, and get a quote. While doing this, check out used sources, especially reputable vendors such as KEH.Com and B&H and Adorama. It's possible that a replacement body will be competitive with a repair nowadays, and possible even that a small upgrade such as to the D3200 would be in order.
If you like the D3100 you're likely to love the D3200, which has a denser sensor, a bit more high ISO capability etc. and the ability to use the IR remote, but is almost otherwise entirely familiar.
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If you don't think you're up to the job the only real alternative is to find a camera repair person or place, and get a quote. While doing this, check out used sources, especially reputable vendors such as KEH.Com and B&H and Adorama. It's possible that a replacement body will be competitive with a repair nowadays, and possible even that a small upgrade such as to the D3200 would be in order.
If you like the D3100 you're likely to love the D3200, which has a denser sensor, a bit more high ISO capability etc. and the ability to use the IR remote, but is almost otherwise entirely familiar.