Firstly, this is the wrong forum. I've moved it for you but please take more care in future. With that said..
I had this same problem on Year 2.
Basically, one of the files on my CD had become corrupted due to a scratch or something on the CD. This resulted in the game not being able to read it while playing, thus it constantly struggling to read the CD but not actually getting anywhere.
To find out which file is corrupted, open up your Grim Fandango directory. Now, copy every file from your data directory on the CD into the one on your hard-drive. If you have indeed got a corrupted file, one of them won't copy across. Once you've found out which file it is, you can take some steps to replace that file such as borrowing a friend's GF cd and copying it from there.
As a side note, if you copy every single file on both CDs into your data directory, you can run the game without having to put the CDs into the drive. This will increase how fast scenes load and such, so I recommend it.