Unfindable Hidden Partitions?

You need to boot the computer from another disk, not the one internal to the computer. If you have the original discs that came with the computer then use them. If you don't have them then you need to have the school provide you with copies or the originals.

Snow Leopard Erase and Install

1. Insert Snow Leopard DVD into the optical drive and restart the computer.
2. Immediately upon hearing the chime hold down the C key.
3. Release the key when the Apple logo appears and wait for the loading to finish.
4. After the installer loads select your language and click on the Continue button. When the menu bar appears select Disk Utility from the Utilities menu. After Disk Utility loads select the out-dented disk entry from the side list (mfgr.'s ID and drive size.) Click on the Partition tab in the Disk Utility’s right window. Set the number of partitions to (1) from the drop down menu. Click on Options button and select GUID, click on OK, set the format type to MacOS Extended, Journaled. Finally, click on the Apply button.
5. After formatting has finished quit Disk Utility. Continue with the OS X installation and follow the directions.
6. When the installation has finished the computer will restart into the Setup Assistant. After you complete the Setup Assistant you will be running a fresh installation of Snow Leopard. Open Software Update and install the recommended updates.
7. Download and install Mac OS X 10.6.8 Update Combo v1.1. if needed. It is not needed if you are selling or giving away the computer.

Once you have the partitions correctly laid out, future OS X upgrades should continue to work, unless you run into future partitioning issues. If you do, please post back on this discussion in the future.

Your steps are correct. If you reboot your Mac, OS X can renumber disks. Please ensure that you run with proper disk slices, if they change. The current Macintosh HD must always be the first in the list of disk slices.

Help for the command is

diskutil mergePartitions

Usage: diskutil mergePartitions [force] format name

DiskIdentifier|DeviceNode DiskIdentifier|DeviceNode

Merge two or more pre-existing partitions into one. The first disk parameter

is the starting partition; the second disk parameter is the ending partition;

this given range of two or more partitions will be merged into one.

All partitions in the range, except for the first one, must be unmountable.

All data on merged partitions other than the first will be lost; data on the

first partition will be lost as well if the "force" argument is given.

If "force" is not given, and the first partition has a resizable file system

(e.g. JHFS+), it will be grown in a data-preserving manner, even if a different

file system is specified (in fact, your file system and volume name parameters

are both ignored in this case). If "force" is not given, and the first

partition is not resizable, you will be prompted if you want to erase.

If "force" is given, the first partition is always formatted. You should

do this if you wish to reformat to a new file system type.

Merged partitions are required to be ordered sequentially on disk.

See diskutil list for the actual on-disk ordering; BSD slice identifiers

may in certain circumstances not always be in numerical order but the

top-to-bottom order given by diskutil list is always the on-disk order.

Ownership of the affected disk is required.

Example: diskutil mergePartitions JHFS+ NewName disk3s4 disk3s7

This example will merge all partitions *BETWEEN* disk3s4 and disk3s7,

preserving data on disk3s4 but destroying data on disk3s5, disk3s6,

disk3s7 and any invisible free space partitions between those disks;

disk3s4 will be grown to cover the full space if possible.

The following command must be run with the order of disks as shown, otherwise you will lose data. A Time Machine back up is recommended, if possible.

diskutil mergePartitions jhfs+ "Macintosh HD" disk1s2 disk1s3

Once the merge operation is complete, post the output of

diskutil list

sudo gpt -vv -r show /dev/disk1

The Recovery HD can be re-built once you have the disk space back, by re-installing OS X, which does not touch non-OSX files.

Please also see Computers that can be upgraded to use OS X Internet Recovery - Apple Support and check if your specific Mac supports Internet Recovery.

For which command? Are you in OS X Terminal?

type diskutil

diskutil is /usr/sbin/diskutil

diskutil list

/dev/disk0 (internal, physical):

#: TYPE NAME SIZE IDENTIFIER

0: GUID_partition_scheme *512.1 GB disk0

1: EFI EFI 209.7 MB disk0s1

2: Apple_HFS OSY-MBP13 380.3 GB disk0s2

3: Apple_Boot Recovery HD 650.0 MB disk0s3

4: Microsoft Basic Data BOOTCAMP 131.0 GB disk0s4

Please post the output of the following OS X Terminal commands.

diskutil list

diskutil cs list

sudo gpt -vv -r show /dev/disk0

Please enter your password when prompted by the "sudo" command.

Change disk0 to disk1. Was the Optical drive of this Mac replaced with a disk or is the Main disk bay empty?

Please post the output of

sudo gpt -vv -r show /dev/disk1