Malware Trouble on a Dimension 4550...HELP!!!!!

       I am having a large amount of trouble with my Dell Dimension 4550 desktop.  I don't know what is wrong with it.  So, I'll give you all the symptoms, and hopefully someone out there can help me.  I upgraded the memory in my computer to a Gig. about a year ago.  That instantly made my computer work wonderfully for a while.  Recently I have been having trouble with about every part of my computer.  First, the computer is acting very sluggish, I have to double click an icon then wait almost a minute for it to finally come up.  All programs (itunes, photoshop, games, etc) have stopped working to their full potential.  Next there is always a large amount of pop-ups.  Every time I come back to my computer there are about 50 pop-ups that I have to exit out of.  And to finally put the icing on the cake, yesterday my broadband internet has stopped working.  I have tried restarting my cable modem, disabling/enabling the connection, repairing the connection, getting new Ethernet cables... I've tried everything that I can think of.  Also I get a large amount of little things coming up in the bottom right hand corner.  Such as SECURITY ALERT, VIRUS ALERT, SPYAXE 3.0, etc.  I would greatly appreciate it if someone could help me out.  Thanks to everyone who reads this!