If you play an illegal Draw 4, then are challenged and fail, do you still get to pick the color? I know the player who got caught playing the illegal card has to Draw 4 cards, but it's unclear if whether or not they still get to pick the color.
As per the (2008) Rules sheet from Mattel (emphasis in second paragraph mine):
Wild Draw Four Card - When you play this card, you get to choose the color that continues play PLUS the next player must draw 4 cards from the DRAW pile and lose their turn. However, there is a hitch! You may only play this card when you do NOT have another card in your hand that matches the COLOR on the DISCARD pile (but it is acceptable to play this card if you have matching number or Action Cards). If turned up at the beginning of play, return this card to the deck and pick another card.
NOTE: If you suspect that a Wild Draw 4 card has been played on you illegally (i.e. the player has a matching card), then you may challenge that player. The challenged player must show you (the challenger) their hand. If guilty, the challenged player must draw the 4 cards instead of you. However, if the challenged player is innocent, you must draw the 4 cards PLUS an additional 2 cards (6 total)!
The takeaway from this: Since the penalty on this states that the challenged player draws 4 cards instead of the challenging player AND since the rules never state that an illegally-played "Wild Draw 4" card is taken back, the card remains on the discard pile and the declared color remains in effect. This means you can't prevent an unfavorable color change from an illegally-played Wild Draw 4 card.
Official Uno Videogames handle this the same way: the Wild Draw 4's declared color remains in effect (at least one version recolors the Wild cards after a color's been declared to make it clear what color the top card is).
Some rule revisions, such as the 2003 Rules Sheet from Mattel, also specifically refer to playing a Wild Draw 4 while still having cards matching the current color as bluffing.
Wild Draw Four Card - This is the best, meanest, most sneaky card to have. Not only does the player get to call the next color played, but the next player has to pick 4 cards and forfeit his turn. There is a hitch, however (of course): you can only play this card when you don't have a card in your hand that matches the color of the card previously played. Note: A player may have a matching number or word card of a different color in his hand and plays his "Wild Draw Four" card.
If a player plays a Wild Draw 4 card illegally and gets caught, he must first show his hand to the player who challenged. If guilty, he must draw 4 cards. If not guilty, the challenger must draw 2 cards in addition to the 4. The challenge can only be made by the person required to draw the four cards.
Notice that the penalty does not indicate the card illegally played should remain in play. The only guidance in the rules is derived from the initial statement that you cannot play this card. The only interpretation I see is to remove the illegally played card from play since it could not be played and to instead play another card. That results in no choice of color having been made. To do otherwise would encourage this illegal play.