HP pavillion laptop running slow.

Hey all!
I recently recieved a older HP pavillion Ze5155, it appears to be a P4 1.8. I got it in trade for setting up a new laptop for a novice PC user who wanted a new laptop.
It had 1/2 meg of ram pc2100 in it so I updated the ram to the max for the machine 1 meg and wiped the drive and put a fresh install of XP on it. It made a difference for sure, But it is still very very slow. Boots slow and runs slow. Ran all the diags on it from HP they say it is operating fine. The deal is the battery is only good for about a half hour to 40 minutes max. Even when on the factory charger this thing runs slow. 5 or 6 minute boot up and when you use the touch pad you can slide down the pad remove your finger from the pad and the pc is still scrolling down the page. Is it possible the battery is effecting the overall performance that bad even when on charge?
I am not a laptop guy and this is the first one I actually ever owned, so I'm not up on any of it. I know I gotta buy a battery but I was hoping that would be the fix. What do you guys think?

I believe a P4 1.8 will most likely not clock throttle so it will use more juice than a standard mobile cpu. Also when batteries age they lose their ability to hold a full charge.

I'm not sure about your slowness issue. Old harddrives often cause slowdown issues but with 1 GB of ram you shouldn't be doing a lot of paging to disk. I would make sure your drivers are correct. Have you had any other issues?

Installed the graphics drivers?

Yes, I have installed even the latest drivers for it. And had no other issues except for the extreme slowness. Since I gotta get a battery I will and then look at a new drive for it. I was also surprised to see 4200 rpm drives I also thought that the drives were 5400...
I really did not know that all mobile processors do not throttle down, shows my limited contact with laptops.
I hate to see this go to the shelf as it can do some stuff I would like to do with it. Watch video and stream mp3 to my older car radio on trips. As for gaming it can do limited stuff, but heck, I got nothing in it except for the ram currently.
Thanks for your help I was beginning to think I had asked a too noob a question for any reply. I have read up about this but missed out I guess on alot of info out there.