My M35-S320 Toshiba laptop has stopped reading CDs and DVDs. What is the problem?

Try rebooting your computer & if that doesn't make any difference then I think there is something wrong with your DVD drive.

If the problem is that you can't see any drives listed under "My Computer" then read this Microsoft article
http://support.microsoft.com/kb/314060

After a while, CD/DVD ROM drives burn out. They simply stop reading media. You will hear them spin, but nothing happens... Usually the lens is the culpri and this is definitely no rare occurrence. It's probably time for a new drive unit.

You can take your computer to any repair shop and you can have them put in a new drive for you, or you can do it yourself. If you want to DIY and since you have a laptop, you will want a OEM drive built specifically for that computer. I would contact the manufacture to see if they can supply you with a replacement. You could also opt for an external hard drive that connects via usb. I recommend www.tigerdirect.com for purchasing parts if you plan to go external. External drives from TigerDirect range from $49.99 and up plus shipping.