Win XP runs perfectly fine with no visible delays with 128 MB of RAM. I'm using a 800 MHz computer with 128 MB RAM and Win XP Pro right now. Startup menu is up before I can blink - no noticible delay. But you must turn off useless features. Turn off the fast user swapping (saves 64+ MB right there). Turn off the screen saver and any desktop image (save another MB there). Turn off features such as the "slowly fade menus into view". That 3 sec delay is a Windows feature!
A 1.6 P4 shouldn't be having those problems. Run the computer as you would for awhile, then right click on the taskbar, click task manager, click performance, and under Commit charge let us know what is there (all 3 numbers). And under the physical memory what is listed as available? With that information, you should know if you need memory or not.
Do you have anything else running that you don't know about? For example, many cheaper computers come with Microsoft Works. In the photo editor of Works there is an "automatic update" feature that looks for updates everytime you log on to the internet. Guess what, it takes 5 MB of memory to do that and it runs everytime you boot the computer. A simple checkbox switch to turn that off can dramatically give you more resources. Search under the OS forum for "processes" and you'll get links to places that will tell you what all of the processes in the task manager do and if you can remove them.
Exactly which applications are sluggish? Sluggish with applications is often a hard drive issue. It could be a slow drive or a poorly configured drive. It could be just about anything, but we don't quite have enough info.
Good luck, time to head home for the weekend.