Beef with old laptop

hello all, my name is dan and im new here. first id like to thank you all for the work you do for free. its places like this and people like you that make the internet manageable, and i thank you from the bottom of my heart.

i acquired a compaq presario 2700 a week ago. its pretty old, i think it was purchased in 02. its basic stats are

intel III 1.13 GHZ
512 MB of RAM

any other info you need (as im sure there must be, i just dont know what) i can provide upon request. my problem is it runs very slow for having over 1 GHZ and seems to randomly shut itself off. it does shut off every time i try to update it thru Windows Update, i know that much, but every other time seems to be random. the last two times were during an online game at Pogo.com and during a Kaspersky virus scan. i was out of the room for the second and didnt get to experience it for myself. i have a desktop with very similar stats that runs great. the desktop has an nVidia GeForce MX 4000 graphics card with 128 MB if that makes a difference.

so, in a nutshell, this thing is old and seems to be running much laggier than i would expect, while randomly shutting off (not shutting down, it skips that part. it just goes off). any ideas or info you guys need, please let me know.

thanks again