When a disc is loaded, the system attempts to read the TOC (table of contents) of the disc. This is the spinning that you hear. If the TOC is not readable, the spinning stops. This will be attempted 3 times (sometimes more). In your case, the disc is not readable. This can be as simple as dirt on the DVD lens or a failure of the laser itself. If you can gain access to the drive, try cleaning the lens (carefully) using a cotton swab and alcohol. This may resolve the problem. If not, then replace the drive.
You can get the laser assembly for around $15 and the entire drive for around $40.