Sounds like it could most likely be something to do with your fuel pump.
1.) Video one may show you why your Honda started the few times it did but stopped .. Electrical solder connection potentially. fast forward to 1:48 http://www.youtube.com/watch?v=viIZ8k60awY
1.)The fuel pump relay is under the dash, in the fuse box. I would also suggest you check the fuel pressure. It should be 2.6 to 3.3 psi with the engine OFF and key ON. If it is a bad fuel pump, there is an access cover in the trunk that allows access to it without removing the fuel tank.
2.) See if this video resembles your start up problem this will cover your relay if there is a problem at all. http://www.youtube.com/watch?v=38DQ5IVQQ68
3.) Testing your fuel pump. This guys video Is a little slow but may help with your problem just fast forward to 1:20 in the video. http://www.youtube.com/watch?v=lOF6nCImxNI
If you need to buy parts I would recommend ebay for to get them much much cheaper than the local auto parts.. Usually comes in with in a few days..
Well let me know what you end up with from there I could help you further! BEST OF LUCK ! :)