It is not every game where you see the hint bug,. You play until you win or see the "No More Moves" window, then end game, play again, or play new game. Mine looks a little different than yours, but it looks like you are not using Aero desktop. Every 1 out of 5 or 10 games I will get the endless hint. Like this:
You play Solitaire and find that you have gone through the deck twice and nothing has changed, there are no cards to play. Just to be sure I didn't miss anything (I might be watching TV at the same time.), I will tap the H button. The deck glows to tap or enter. Next card comes up, no moves to play. Tap H again, deck glows, no moves. Rinse and repeat, several times, give up and close game.
Sometimes I will miss a move, but when it becomes apparent, anything, even moving a card up to the stack deck top right, I would have to run all the way through the play deck again before hints should show me there are no more moves. And it does not happen. It is ridiculous and funny, you tap h, deck glows, advance card, tap h, deck glows, until you reach the end, then the empty deck glows, reset the deck, tap h, deck glows, next card, tap h, deck glows, until you reach the end of the deck again. After going through the deck twice, with no moves at all, the game should end and it does not. The hint button keeps you cycling through the play deck, forever.
Not every game. Out of 10 games for sure I will see this at least once, usually 2 or more times. Windows 7 Ultimate, 64 bit.
This is a silly issue, not a serious one. But we come to expect perfection from our PCs and when it does not happen such as in this case, it is unsettling. And it is not like Microsoft would ever "fix it". They have already taken it out of Windows 8 and 10 and charge you for it, forever, if you wanted to play Windows Solitaire.
EDIT: If this is a real bug, I should be able to Google for it and am not having good luck, cannot find anything on Google about this. But I have been frustrated by it for months! Go figure.
EDIT 2: Tell you what, next time this happens, I will try to grab a FRAPS video of it and put it on youtube. Then you guys can see if there is a play on the board that I just do not see. I doubt it since the hint keeps cycling the play deck and nothing else.