You can blow some can air in the dvd rom drive itself Sometime's that will clear the laser enough to make them functional again. If not they are generally about $20-$30 to replace them with a dvd burner.
You could try looking for an updated driver on the E-Machines website. You might also want to contact E-Machines technical support for troubleshooting as there may be a physical issue.
If the machine is still under warranty, you can replace it. If not, replacing a DVD drive is simple; a few cable connections and a screwdriver are all you'll need.
More than likely your drive has died. They are cheap enough that you can just install a new drive. They are pretty easy to install. Just make sure you buy a quality brand.
