I have 250GB Seagate External Hard Drive and it will not show up on my PS3 when I connect it. It is currently in a NTFS format but do I have to change it to FAT32 to get it to work? It doesn't even show up on the screen once connected to the PS3 either. Can anybody help me?

Having experienced this and done research:

To get an external drive to work with the PS3, it must be formatted as FAT32 before you connect it for it to recognize it. You can use it to play media files (saved from your computer) on the PS3 or use it to backup stuff on your PS3.

If you browse the internet using your PS3, you can also save things you may find while browsing, such as documents or setup files.

you can only use an external hard drive to backup your information (for ex. music, movies, games saves, downloads)
1st you need to reformat the hard drive to the file system of the ps3.
The way you do that is to go to settings, go down to system setting, hit X
go down to format utility and it's going to give you the option to format the external hard drive.
Follow the same directions from above and instead of going to format utility go to backup utility and then press X on backup. But if you already have a backup on the external press X on Restore.

The only way you can upgrade your hard drive space is to install an internal 2.5 in. SATA hard drive.