I fixed my NES by doing steps similar to these (blowing on the kart does no good)
http://home.centurytel.net/wcp/nes/

Step 1
The first thing you need is a Philips screw driver to undo all the screws, an eraser (it's better to use one on the end of a pencil) or toothbrush (preferably not yours) some electronic cleaning solvent (Windex, or a 50/50 mixture of Rubbing Alcohol and water work fine as well) and a whole mess of Q-Tips remember to unplug the NES and turn it on to remove any electricity.

Step 2
Now you need to turn it over and undo the six Philip's screws, then holding it together turn it back over and take the top off this will leave you with a big silver cover show in the picture below.
(The Numbers are where the screws are)

Step 3
To take the silver protective cover off there a seven screws holding this down.
(The Numbers are where the screws are)

Step 4
Now unscrew the games slot and the RF/AV and Power box.
(The Numbers are where the screws are)

Step 5
Now lift the main board out and pull out the two controller leads and and Power/Reset Button lead and turn the board over.

Step 6
The three leads have been removed and the board has been taken out, yet another silver cover to be removed.

Step 7
Now to pull the black connector off of the main board and you will see the silver pins which it attaches to.

Step 8
Now use the eraser (or toothbrush) on the silver pins where the 72 pin connector was and get it as clean as possible. Now get a Q Tip and spray each end with some electronic cleaning solvent and again rub it on the silver pins where the connector was. If done right will make it like new, now take a dry Q Tip and rub any solvent left on the pins off. If you have done all this and it still didn't help you will need to buy a new 72 pin connector either from eBay (give or take $10) or MCM Electronics ($7.99) (USA Only) If you're exceptionally careful, you can clean the 72 pin connector with the solution and a pair of fine tweezers or paperclip with something to scrub them at the end.

Step 9
The NES is now all put back together and like new except the the 72 pin connector (unless you replaced it) this can easily be cleaned if you have a "Cleaning Kit" by Nintendo which can still be bought from there web site. www.nintendo.com. If you don't feel like it, however, you can try either the way suggested above, or cut a piece of folded over cardstock to the proper size, put the cleaning solution on the end by the fold, and insert and remove the cardstock from the 72 pin connector inside. This isn't a very good method, however, and I suggest either buying a replacement 72 Pin connector or using the NES Cleaning kit.