Start the game with the command-line parameter "+set developer 1" to enable the cheats. While playing, press [~] (tilde) to bring up the console, then type any of the following cheat codes.
Example: "C:\Medal of Honor Pacific Assault\mohpa.exe" +set developer 1

Note: Make sure you use this parameter with the mohpa.exe file and not the mohpa_setup.exe file which is installed to your desktop by default.

Alternate Method
Instead of using the command-line parameter, you can edit your player config file, located by default in "My Documents\EA Games\Medal of Honor Pacific Assault\configs". The default file is "unnamedsoldier.cfg". Open this file with notepad Add the following line seta developer "1" at the bottom.

Save the file. This should enable the console once you go back into the game. Still use [~] or [¬] Key to bring it up.

Code - Result:
noclip - No Clipping Mode
fps 1 - Show FPS
dog - God Mode
wuss - All Weapons
fullheal - Full Health
notarget - Enemies Ignore You
maplist - Load Any Level (double-click map name)
map [mapname] - Load Map [mapname] (use names from maplist)

Second Method
If you still cannot get the console to come up, you can actually bind the cheats to keys using the config file which does not require access to the console. Open your config file with Wordpad.exe (located by default in "My Documents\EA Games\Medal of Honor Pacific Assault\configs"). The default file is "unnamedsoldier.cfg". Under the // Key Bindings section, simply change any of the bindings to the cheat codes. For example:

bind F1 "dog"
bind F2 "fullheal"

Then, while playing, each time you press F1, you will have god mode, F2 will give you full health, etc.