.. What is the password for the computer?

It's somewhere in the office, and why on earth couldn't Melina just have told you the password when she called? Twit.

As it happens, it's on a bright yellow sticky note --

-- inside the locked filing cabinet. Grrr!

Where is the filing cabinet key?

After you open the filing cabinet, look at the sticky note inside the left drawer.

The password is KLEROTERION, but it won't work until you read the note for yourself. (A kleroterion, by the way, is a device used in ancient Athens to randomize jury selection. It's pretty cool, if you want to check out the Wikipedia entry: #h+https://en.wikipedia.org/wiki/Kleroterion#h-)