It says "last received block was generated 883 days ago" and blocks remaining number stopped. On bottom left it says "Reindexing blocks on disk".
How can I move my bitcoin address from Qt wallet 4.8.3 to BitcoinCore?
Qt 4.8.3 is NOT A VERSION OF BITCOIN CORE. That is the version of the GUI framework (Qt) that is used by Bitcoin Core. 4.8.3 hasn't been used by Bitcoin Core in a while, so you are probably using 0.9.x or earlier.
You are using old software. I recommend that you first upgrade to the latest software, Bitcoin Core 0.12.1. Let that run and see if that has any issues.
Can you provide the debug.log file?