How doI unlock my CD & floppy disk drawers which refuse to slide open?

Most CD-ROM drives have a small hole on the front on them. Un-ravel a
paperclip and insert one end of the paperclick into the hole on the
CD-ROM. Push Hard and the CD tray will pop out. As for the Disk
Drive... The button on your pc case might be broken.. You might want
to try removing the casing on your pc and take a look.

I know it's not a complete answer but i hope it helps.

Do you have media stuck in these drives?

If not I'd throw away the floppy disk drive and invest my money in a USB key.

http://www.pchardware.co.uk/usbkeydrive.php

They can hold more data and a less likely to become damaged.

To open a CD drive, do as sw33t says and use a paperclip.  It is very
important that you remember to 'straighten' the paperclip first, or
the technique will not work.  Find a very small hole on the front of
your CD drive, and push the paperclip into it, holding it as straight
as you can.  This does require some force, so don't be afraid that you
will break it.  The manual gears will turn, and the door of the tray
will open just enough so you can grab it with your fingers and pull it
all the way open.

Floppy drives are a little more tricky.  You can try to open the
floppy drive door with your finger and use a pair of small
needle-nosed pliers to lift up on the disk and pull it.  This rarely
works however, as the metal cover for the magnetic disk is engaged
inside the drive, and does not release.  The other solution is to
remove your floppy drive from your tower, first remove the front bezel
by depressing the small tabs on both sides of the drive near the
front, and then locate the 4 small screws that hold the top and bottom
pieces of the drive together.  unscrew those 4 screws, and remove the
top portion of the drive, this will give you access to the disk.

Try using a flat head screw driver to carefully pry the drive open. 
It sounds like the drive is broken, can it read the disk (if there is
one) in the drive?

sw33t-ga is right, if there is a cd in the drive then it may be worth
it to remove.  Otherwise you should probably throw it out and get a
new one.  Floppy and cd drives are not expensive.

Another thing you could try is to take the drive apart and then throw
it out once you removed the media.  If you do that you should not to
put it back together and use it.

this accually happened to me for awile it turns out there was a
spyware program doing this jamming both drives i sugjest scanning for
that first