I think this situation is covered by 2 assumptions that may not have been adequately articulated before:
1) If you are instructed to draw a card and cannot, you don't get to draw a card. The rest of the card takes effect normally.
2) The cards which require you to discard 2 cards give you no benefit if you can't discard the 2 cards -- those discards are the "cost" for playing that card, in effect.
Thanks for your reply. This should work now as described.