I do not see a valid reason to install another software as InDesign is a great tool for digital publishing.
I have tried to save a .jpg document with both of your dimensions 851x351 and 851x315, and did not notice any issues in InDesign. Make sure you have the latest version of InDesign installed and you use File->Export->JPEG->Export command.
It sounds that it is a problem on the side of your PC not InDesign in this case. You can check couple of things:
- You have enough free space on your drive (as suggested in comments) and there are no bad blocks and SMART status is healthy (run diagnostics on your drive).
- The dimensions are set correctly, in your case it should be 70p11x26p3 (as suggested in comments).
- You are running up-to-date version of InDesign.
- You are running up-to-date version of Windows.
- You have enough RAM.
- You can try closing all other currently open resource consuming software so that InDesign will be the only software running at that moment.
There can be more suggestions on what you can do, based on your responses to the mentioned above steps.