Can I find the address of my Bitcoin in the debug.log file? I cannot download the entire block chain (I’ve tried four times now and failed) so I can’t replace my encrypted old wallet.dat file into  the blockchain and do the rescan to check my coin balance. My question is, can I find my Bitcoin address in the debug.log file. Is there a way to use the information in this file to check my Bitcoin balance?
Any addresses will be in the wallet.dat file and can be viewed or extracted without any need to download (synchronise with) the whole blockchain.
You can check the balance of an address by using several different public blockchain explorers and checking the results are consistent.
See also

dumpwallet output documentation &amp; explanation?
What do the different .dat files contain?