Apparently it can be upgraded up to 5GB with one spare slot that currently sits empty.

I found 2 physically compatible identical 2GB modules but no matter which one I plug in, when I start the computer it just starts the fan on highest setting and nothing else happens.

Before I go into any more detail, I found this info online:

The Toshiba Portege R600 Laptop takes the PC2-6400 DDR2-800 200pin SDRAM SODIMM memory type

My sticks look like this:

Are they compatible to PC2-6400 DDR2-800 200pin SDRAM SODIMM? I honestly can't tell.

I read the manual which says the modules need to be "Toshiba approved" but it does not say which/what Toshiba approves.

Plus this, which I did follow (note the negative):

Do not try to install or remove a memory module under the following conditions.

a. The computer is turned on.
b. The computer was shut down in either Sleep or Hibernation Mode.
c. Wake-up on LAN is enabled.
d. Wake-up on Wireless LAN is enabled.
e. The wireless communication switch is turned on.

And this does not happen:

If you install a memory module that is not compatible with the computer, the Power indicator will flash (on for 0.5 seconds, off for 0.5 seconds) in the following way;
■ If there is an error: repeatedly flashes orange twice, then white or green once

The power indicator ⏻ stays white all the time and does not blink.

TIA