take the seed, place it in between your fingers.. and try applying pressure to the seed. Don't put too much pressure on it.. but enough to test its viability.
If it smashes in your fingers, its no good. If its able to withstand the small amount of pressure.. its good to go.
Also, another way to make sure seeds are good.. and viable. Is to visually inspect the seed with your eyes. The ones that are good, will be a dark brown color.. with black stripes (kinda like tiger stripes). Those are the best ones..
Here, here are what good seeds look like.
View attachment 983527
See how the outer shell of the seed looks?? Those are the ones you want to look for.
As far as the white hair thing you've described. I ran into this problem not long ago.. I went ahead and planted the seed.. and it came out just fine believe it or not. I would just go ahead and plant it.
Also, another thing you could try.. is put the seed in a glass (like a drinking glass) and put it under the sink faucet.. and blast it with a little water.. not too hard though.. just enough to try and wash off the fungus.
Good luck!
Oh, and like Whiteflour said, the paper towel method isn't the best method to use. I prefer either soaking the seeds overnight in a glass of water.. until the seed swells up and pops open. But, you gotta keep checking on the seed every 12 hours or so.. because once it does pop open, it will need to be removed from the water ASAP as to keep the seeds root from getting too soft. Which will cause problems.. such as causing the seed to not sprout. As soon as you see that the seed has popped open, immediately plant the seed into your grow medium.
Another good germination technique.. is to use a cloth towel. Similar to the paper towel method... but better IMO.
Good luck man.