Most probably it cant find where the games are stored and is assuming you have simply forgot to put a disk in.
Have you checked the hdd games are still intact? If they are and steam is still pointing to them you could see what it says when you click check game registry (im not at a computer right now, i think if you rightclick the game on steam and swlect properties you will be able to see the necessarys.

thenumberone : Okay, I tried and clicking absolutely anything in the box makes a new popup saying "The name 'F:SteamSteam.exe' specified in the target box is not valid. Make sure this path and file name are correct." same thing for all of my games.

Is your "memory box" (This is called an external HDD, by the way) plugged in? If so, click the Start Orb (If Vista or 7) and click My Computer.

You should have at least Local Drive (C:) (Or Acer or HP or something depending on your computer), your DVD drive might show up, and you should see your external drive in there as well. If it's labeled as (F:) then Steam should work. If not...

BEFORE CONTINUING MAKE SURE YOU KNOW THE NAME OF YOUR EXTERNAL DRIVE. IF YOU REMAP THE WRONG DRIVE YOU COULD SERIOUSLY MESS UP YOUR SYSTEM

Make sure your Windows account has Administrator access, then click the Windows orb and type "computer management" (Without the quotation marks).

In the left pane of the window that opens up, find the Storage Tree, and open it to find Disk Management (if it is not opened already).

In the Disk Management screen, make sure no other disks are marked as F: There shouldn't be any since it is asking for a disk.

Find your external drive. AGAIN IT IS VERY IMPORTANT THAT YOU KNOW THE NAME OF THE DRIVE AND DO NOT REMAP THE WRONG DRIVE!!

Right click the external drive and click Change Drive Letter and Paths...

This will open another window. Highlight the drive, and click the Change button.

In the window that pops up, click the dropdown menu, find F: and then click OK

Steam should work now.

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What happened here is probably at some point you had your external HDD unplugged, and had a USB stick or something else in your computer that took drive F:, and while it was plugged in, you must have tried starting your external. Since F: was taken, it grabbed another drive letter, because typically you do not have programs or other files where drive paths are important on external drives. Once it was marked as F:, every subsequent time you plugged in it, it kept the new letter, and Steam didn't know where to look. Since it always found the files in drive F:, it didn't know to look somewhere else.

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If this doesn't help, let me know. Make sure you keep a detailed account of everything you do so I can see if you missed any steps or didn't understand anything.

Lazlo Falconi : Thank you. I'll try that as soon as I can. (I know the name of the drive, don't worry.

I'm just posting here so you can reply. Did it work?

Lazlo Falconi : No, but I did solve the problem. I'll send you some Viz for your trouble though.