The problem is that JDM's are rubbish - they require the serial port to exceed the RS232 specification.
One solution is to change your computer to an old one that works with the JDM.
I've never considered the JDM as a 'real' programmer, it was a VERY clever project to make a PIC programmer with a minimum of components, with no thought for how reliable it might be. Unfortunately many people (like yourself) saw the simple design and built it, and for a good percentage of people it never worked because it's not a good enough design.
Notice my software WinPicProg ONLY supports parallel port programmers, even though it would be trivial to add serial port ones to it - this choice was specifically because of the JDM's poor reliability. Unlike most other authors I provide support for my software, and I wasn't going to get involved in the huge numbers of non-working JDM's.
Anyway, it's all academic now - don't mess with serial or parallel port programmers - get a PICKit2 or clone, like the Junebug.