I think that the 36 pin connector would not be a problem, just use the corresponding pins. Electrically it should be the same.
However, I don't think a USB-parallel adapter will work, because software like avrdude uses parallel port registers which are not provided by the USB adapter. You would need a real parallel port on a PCI card for it to work.
I can't confirm or deny the theory since I haven't tried it, but first I would see if avrdude can recognise the adapter. I would think the best thing is to get a refund on the adapter.
However, I don't think a USB-parallel adapter will work, because software like avrdude uses parallel port registers which are not provided by the USB adapter. You would need a real parallel port on a PCI card for it to work.
I can't confirm or deny the theory since I haven't tried it, but first I would see if avrdude can recognise the adapter. I would think the best thing is to get a refund on the adapter.