You can force a shutdown in the command window. But when a pc doesnt shutdown accordingly I would too suspect something like a virus or other malicious software.
Remove ac adapter , then remove battery. no problem I do this many time .
Want more speed : switch system to classic theme . Update OS and antivirus (Automatically detect and install latest best driver and fix all issues). Full Scan with "SUPERANTISPYWARE" pro (after successful deleting virus uninstall this) . Use game booster software (freeware) for disable some useless services . Update bios and hdd firmwares . Oc system . Etc...