I've used PSP since the first version which, if I remember correctly, didn't even fill a floppy disc! I'm not sure which version started supporting transparency, but it was a long time back so it might be available in PSP3???
Check under Colors to see if you have the Set Palette Transparency option. If you have ...
Your graphic will have to be limited to 256 colors, so you may first need to use Image/Decrease Color Depth.
The easiest way is to set the transparency to set it to the current background color. Remember if the color you select as background is included in your graphic, that piece of the graphic will also be transparent. To avoid this use Fill to color the background, opting for an unused color. (Magenta is often a good choice!!!)
You'll need to save it as a GIF and will need to use GIF89a interlaced. Use Options in the Save As GIF dialogue box to select the 89a interlaced version.
Fingers crossed. <G>