Dvd drive assingment

Have you tried a system restore ?
Or uninstall and reinstall it.

Have you recently uninstalled any CD/DVD burning software?

It's kind of weird you don't mention a D: drive. Typically A: is floppy B: is second floppy or reserved for 5 1/4" floppies that they do not make anymore, and then C: is the main drive. Since you have a laptop, there cannot be a second hard drive internally (except maybe an SSD drive in new laptops) to take the D: drive letter, so you would expect that your optical drive would be D: not E: unless you changed it yourself in Computer Management\Disk Management. If you only have one hard drive then the OS would tag the optical drive as D: and any external USB drive letters would follow as E or F etc.. Another puzzler is you mention H: as your recovery drive which is very unusual. Recovery Partions are typically hidden from view even if you choose show hidden files and folders and system files. If for some reason you changed the drive letter of your D: optical drive to E: manually, try chcnging it back to D: and see what happens.
You can also go into Device manager and uninstall the drive and reboot to allow Windows to reinstall the generic drivers. Virtual drives, like Daemon tools and Nero image dribve will also take up drive letters but normally they would follow D: unless you change it yourself. I have sucessfully changed drive letters for optical drives with no issues though, like Sony DVD would be S: and Plextor P:. That allows my virtual drive to get the D: letter when I install it, and makes for a lot less problems when using virtual disks.