Bitcoins lost in Bitcoin Core?
In bicoin-qt open Help > Debug Window > Console.

An type the following commands.
First you need to list all addresses with funds, look for every line that has an address and take note.

listuspent


Second, you unlock your wallet

walletpassphrase "YOUR-PASS-PHRASE" 120


Then for each address, you should get the private key

dumpprivkey "1BITCOINADDRESS"


take note of every private key and  import them in another wallet. Take care when handling private keys and don't save them in clear text.
Instead of having an online wallet, what you can do is install Electrum which is a SPV wallet and import your private keys there.