Transactions from Bitcoin-qt wallet not entering the mempool
There should be a file called wallet.dat. It contains your private keys which allow you to send your BTC.

Warning: Before you do anything with the file create at least one backup of it. Do not send, upload or otherwise share the file with anyone. Who ever has this file can spend you UTXO (steal your bitcoin).

Since the transactions both did not propaganda you can safely send them again. There are two ways you could approach this:




Using a new version of bitcoin core


download and install bitcoin core v0.15.0.1
start Bitcoin-qt v0.15.0.1
let the blockchain sync (this might take a while)
stop Bitcoin-Qt, copy your old wallet.dat and replace the new wallet.dat in the bitcoin v0.15 directory, start Bitcoin-Qt
you should be able to send the transaction 






Using Electrum to sweep the private key(s)


download and install Electrum
create a new standard wallet and from a new seed
write. down. the. 12. words!
open your Bitcoin-qt v0.8.5
navigate to help > debug window > console
type dumpprivkey [your Address] (repeat multiple times if you have more than one Address)
copy the private key
in Electrum go to Wallet > Private keys > Sweep
paste you private key and click on sweep
Electrum sends the BTC to your Electrum wallet



Both methods should work for you. However since 2. is faster (no blockchain download needed) and you already considered switching to Electrum, this method might be preferred. 

Edit:
Don't delete the wallet.dat after you send your BTC. The private grants you access to the same amount of BCH (Bitcoin Cash). One BCH is at the moment worth 7-9% BTC or about $600.