I absolutely hate diagnosing power issues on computers. While WinXP has the best support for power management (PM) of any of the Windows versions, there are virtually an unlimited number of causes for the problem you are describing. PopTray 3.x really isn't the actual cause of the trouble you are seeing though it is contributing to what you are seeing. What I mean is that PopTray on good hardware without other odd acting software will operate just fine as long as all of the equipment and software is setup correctly. Trying to find PM problems isn't for the week of heart as you may have already found out when you got the rest of the power stuff working at least part way.
Since I'm not actually working with your computer, all I can do is make some suggestions for you to try some of which you may have already done. Any one of these or any combination of them may be part of the cause. Try these in any order, I'm going to try to list them in the most likely to the least, such as configuration issues first. Oh, one other thing, the older or cheaper the equipment is, the more likely you will have these types of problems with PM stuff.
(If you don't want to try all of this, I'd certainly understand, but if you want to find out if it can be fixed you don't have a choice). When trying to pin problems down, it is best if you can 'divide and conquer', in other words, turn off and disconnect everything that isn't needed to connect to the internet. The only things you should have connected is your monitor, keyboard, mouse and what ever you connect to the internet with (network connection, modem etc). After you have done this (and after each thing you try for that matter) test to see if the problem still exists, if it does, continue to the next part, you can reconnect or re-enable everything later.
1.) Check your BIOS PM settings, such as making sure it supports ACPI settings etc. Look at the device you connect to the internet with, like the network card, USB, or modem and see what IRQ it is using. Then make sure that your BIOS isn't set to monitor that IRQ or the modem. (if your computer is watching the IRQ for activity it can keep your computer going as long as there is activity there.)
2.) Disable all other running software including your antivirus and other protection software. (If you do disable your protection software and after testing it still doesn't work, turn them back o (re-enable ) ASAP, no need to open yourself to other problems, as to other software leave disabled for now and re-enable later).
3.) Take a break, the next step is kind of lengthy unless you know where to get it all already. A sandwich may be nice about now.
4.) Get the latest BIOS update for your motherboard and apply the update. While you're on the MB website, get the latest drivers for the mainboard such as the chipset drivers, USB, AGP, sound or other drivers that came with your motherboard. All other drivers that you need will have to work from these base drivers that your MB has.
5.) Update all other drivers for your computer, like video, sound, modem, network card and any other add-on devices. If while updating drivers you get a message about you installing an older version, keep the newest versions. If on the otherhand that it says that the driver isn't tested for XP, don't worry about it and go ahead and install them.
If you are still having problems, I'd probably give up at this point myself except for one other possibility. If your Windows install is an Upgrade install you may have some leftover 'crud' from the original Windows that you had upgraded from. If so there is only one certain way to get rid of these types of problems. Re-Installing WinXP fresh. You will need to backup all of your data you want to keep, documents, spreadsheets, databases, email address books etc. Locate all of your program disks (including your old Windows CD so the Upgrade CD will be able to verify that you qualify for an upgrade). Next do a complete reinstall of your computer, remember to have the setup do a format of the drive, don't try to have it keep what is on it because you can't trust it. There are a lot of places on the internet where you can find instructions for that. Just remember that you need to have all of your CD's and drivers handy before you start this.
Good luck with the rest...