Hmm weird...must be something to do with what the games are looking for when you place a CD in that drive, and obviously, its not finding anything, so thinks the cd's not in it needs...
Something leads me to believe this could be something to do with the cd drive not spinning up fast enough to deliver the codes to the game to know the disc is in, in time, especially if that hard drive is faster than your old one.
Make sure the CD Drive is set to Master inside your computer which might help this, and might also make the cd recognise it better.
Plus, when putting the disc in the drive, wait for it to start spinning up, and then press the EXE file.
Does it work then? This would definietly proove my point right.
and finally try this,
most games have an exe file to boot it up from within the cd drive. Try using this as well
i hope this helps