Some of the most common parts of carts failing/not working are due to 2 things. One being
  the carts pins have started to oxidize or have corrosion taking place, causing contact to not
  occur well. The beginnings of oxidization of the pins can sometimes not be seen well, but
  as it progresses you can see the damage easily. You will need the proper security bit to
  open the cart, and typically a bit set can be found on ebay in the game area or elsewhere.

  In the case of oxidized or corroded pins you can lightly sand the pins down using a light
  grade abrasive sand paper, or steel wool once you have the cart open. Sand the pins on
  each side of carts pcb until they basically have a light shine to them again. After doing so
  clean them with a rag or q-tips and alcohol. If the cart still will not work after this procedure,
  then its possible the problem is caused by the other common issue, a dry cap. If the cap
  has failed it can cause problems for the game cart. You will need to check the value of the
  cap and obtain a replacement, from Radio Shack or Parts Express, or where ever you obtain
  your components usually.

  You can either desolder the cap, or just twist it off and solder the new ones legs to the left over
  pins, entirely up to you. Just make sure that the solder points are solid on the back of the cart
  still if you just decide to twist the old cap off and reuse its legs as a solder point. After you are
  done soldering clean up the solder areas with q-tips and alcohol, put the cart back together and
  try again.

  If neither of these two common fixes help your issue then its possible your system cart slot needs
  to be cleaned, or simply that the carts chips are dead, which is uncommon, but can sometimes be
  the case, and you will be on your own there. Oh and yes, the sand paper trick can be used on
  Hu-Cards too. :P