How can I use/convert the touchpad, keyboard and screen of an old laptop to use them with a desktop PC?
A laptop screen is usually an LCD screen with an LVDS connection (or two depending on resolution.)  This is a differential parallel data bus with data pairs and a clock pair.  The protocol is not too complicated, but you won't be soldering directly to a desktop compatible video connector without an interface board.  LVDS is pretty standard, but an interface board for your specific LCD panel will provide the proper drive voltages for the LCD and backlight.

If you search for your LCD panel, you may be able to find a controller board that will run the LCD as a desktop monitor.  That is probably your best hope, if you don't have the capability of making this yourself.

Most laptops typically have USB or PS/2 based keyboard and touchpads, although some are raw devices.  For USB style or PS/2, you just need to locate the place to connect all wires and you should be set.