Hi
Here is an image that will allow you to install OSMC from USB. You can either manually dd this to a USB stick, or using the official OSMC installer, select ‘use local image’ and navigate to the file.
If you have a faulty SD card slot, we would be happy to look at the unit and replace it. But this should hopefully get you up and running and let you watch some TV over the weekend. I think the issue is that you were putting in the SD card upside down however.
Cheers
Sam