If the disc won't spin, you're out of luck. The only option there is to replace the GD-ROM drive assembly, and since it was a proprietary format, nobody is allowed to manufacture replacements. Some websites do sell refurbished drives for the sake of replacement, but they are pricey and cost the same as purchasing another used Dreamcast.
The GD-ROM drive in the Dreamcast is a fickle piece of hardware, and is faulty in just about every system. In most cases, after sufficient use, the drive has a harder time reading the discs. Follow the instructions
here if you have this happens to you and it boots to the BIOS screen instead of into the game. The fix is moderately easy. You only need phillips drivers to open the box and get to what you need. The actual fix itself is turning a tiny screw up to 90degrees to adjust the disc rotation speed. After your initial adjustment, it is trial and error until it works, or you get frustrated.
To answer your question:
It is easy to open the Dreamcast.
Your problem (no disc spin) is not easily fixable. Another Dreamcast could be had for cheaper ($20-30 for a used DC) than sending it out.
Disc read errors are a common problem with a moderately effective fix.
Come to think of it, it isn't a bad idea to have a spare either. I've got three units in my possession, but I'm also sort of a Dreamcast freak. I have performed the fix I mentioned multiple times on different units, and it worked every time for me.
Good luck!
and please don't dump the broken unit. Its a beautiful and artful case. I bet you can figure out something, like
make a guitar and
matching amp.