I've been solo mining with cgminer 3.12.3 and now updated to 4.3.4.
However, the same setup (BITMAIN AntMiner U1) which worked on the earlier version, no longer seems to work on the new. (Startup simply: "cgminer.exe -u blah -p blah -o 127.0.0.1:8332")
Did you tell it which bitcoin address to mine for?
If not read the readme.