Shorena is right, if you paste that long string here that you get from getrawtransaction you will not be leaking anything that will allow anyone to steal your bitcoins.
However, if you prefer to try to handle this yourself for now, there are two other places that will relay the transaction to the network for you which you can try.
One is the blockr.io block explorer. You can paste the string at this link to use their service:
https://btc.blockr.io/tx/pushThe other is a mining pool. You can give the transaction directly to them at this link:
http://eligius.st/~wizkid057/newstats/pushtxn.phpNote: It sounds like your transaction is made up of MANY VERY TINY VALUE outputs. This typically happens from using "faucets" or other "free bitcoin" services. Depending on the fee settings that you have set up on your wallet, there is a chance that your transaction doesn't pay a high enough fee and that most nodes on the network are therefore refusing to relay the transaction. If you decide to paste the transaction here, we will be able to look at its structure and better inform you of any potential issues.
