If you have a wallet.dat you can open it with an offline bitcoin core, then use the instructions in the quote to export private keys from it and import them into an electrum wallet. Electrum can give you almost instant access to your coins.
Click file, then receiving addresses. Find the address you sent coins to in the window that opens, right click it, and select copy address. Close the addresses window.
Click help, then debug window.
In the debug window that opens click console.
In the text box at the bottom of the window type
dumpprivkey
yourAddresswhere
yourAddress is the address you sent coins to and copied earlier.
Press your enter key.
The private key for that address should appear in the console window. Copy it.
This is an example private key.
L48toSntMVhC2az4KAQCWscrQGfPbT55yCgzM5cmx9Ao69pTdwrq
Download and install electrum.
https://electrum.org/#downloadImport your private key into it using these instructions.
http://docs.electrum.org/en/latest/faq.html#can-i-import-private-keys-from-other-bitcoin-clientsAfterwards your coins should be spendable.