Well, lets see...
   Gateway... not bad.  They're good about upgrading.  Open the case, and it's all nice and clean in there.  1100Mhz isn't that bad.  Anything above 800 is basically just for play and graphics rendering... I doubt you would notice much difference, but take it if you can get it.  128 MB memory is a bare minimum... you'd be wasting money buying a new computer with less... even if a new computer, for some screwed up reason, was to actually COME with less.  FAT32 is a standard now for Win9X/ME.  It's basically just a better use of clusters... Win2K works best on the NTFS system though... but since this is *sigh* WinME, you don't need to worry about that.  20GB Drive?  Umm... yeah, that's alright, but it's like going shopping for a Cadillac and buying a Chevette.  20GB is a barebones hard drive these days.  You can (or should) look at something a little more spacious.  48X CD Rom isn't bad for basic CD reading.  When I bought my first computer, the fastest you could actually get was a 4X.  Again though, 48X is about as small as you're going to get in a new computer without it coming with a hand crank.  Look for a CDRW or a DVD and at least shoot for something modern.  Speakers are speakers.  If they suck, you go to Radio Shack and get a better set for $9.99.  The BEST computer speakers, IMO, are house speakers.  56K Modem leaves a lot open.  Is it a 56K v.90 Flex?  Voice?  Fax?  If it's a basic 56K Internal modem, the going cost is about $15.  Once you start adding fancy shit to it like built-in fax capabilities and a voice answering machine, the cost can get anywhere up to $60 or so.  The keyboard sounds like a standard Keyboard.  Nothing flashy there.  Same with the mouse.  The 10/100 Integrated Network might be nice, though.  That means that a card has been installed that will allow you to add this computer to a network (have other computers share it's resources, and even it's internet if set up properly).  PC Doctor is alright.  Problem is, it only catches what IT knows is wrong.  Nothing beats personal know-how.  Now... the Operating System.  See what you can do about having that replaced with something, well, better.  If they won't do it, you'll need to go and do it yourself.  I would suggest a complete wipe of the entire OS and a nice shiny new stable decent one put in it's place.  1 Year of AOL?  They should be paying YOU for this one.  But since you're already an AOL subscriber, it's no loss on your part, right?  Norton Anti-virus isn't that bad.  It tends to miss some things, and in a lot of cases a computer company will install a bare minimum of it when they sell a new computer... basically something to cover the computer until you get it home.  Start shopping around for something better soon.
   All in all, I would say (given the fact that someone has stripped this computer down to the basic minimum's in pretty much everything) $699 tops.  You could spend the extra $100 (bringing an estimate to $800) and get a fully decked out computer from somewhere else.  Of course, this is all just in my own opinion... but unless you're just wanting a computer that will play sound for you, I would spend my money on something that was actually worth the cost.
   If you actually want a decent computer that costs a decent amount, let me know and I'll track one down.  Otherwise, this is going to have to be your call (but make sure you're going to get your money's worth).