Task Manager won't come up

 When I boot up my Inspiron 1100, it is very sluggish and the "hide icons" arrow on the lower right system tray does not come up right away (5% of the time it does not come up at all).  After my PC is booted, I am unable to open Task Manager.  When I try to start Task Manager (either by right clicking the bottom bar and selecting Task Manager or by pressing ctrl-alt-delete), it comes up for approximately 1 to 2 seconds, then disappears.  It's icon does appear in the lower right system tray, but when I move my mouse over it, the icon also disappears.  Much of the time the icon shows 100% in use (the icon turns 100% light green). 

Of course, since I cannot get to the Task Manager I cannot go into "processes" to see what is eating up the CPU usage, or to see anything else.   What is the problem?  Is my PC dying? Is my OS (Win XP/Pro with all  patches installed) corrupted?  Could some hardware (e.g., hard drive or RAM or BIOS) be damaged resulting in the OS not operating correctly?  I need my Inspiron to do my job, so this it is vital that I get control of Task Manager (and the rest of my PC system) back.
                      
So, what is wrong?  What can I do?


Details: Model: Dell Inspiron 1100, Purchased 03/2003, CPU - Celeron 2.0 Ghz, RAM 512Mb, OS Windows Pro, Harddrive 30 Gb (with plenty of unused space on it still).