Why does the Computer shuts Down "Immediately" (during power Cut off)?

A few months ago my 500 watts smps stoped working. So i got a 450 watts smps instead as 500 watts was unavailable. And before that few monts ago my ups battrey was also damged so i replaced the battrey too. Since than my computer shutsdown instantly at power cuts and sometimes it don't, (it works fine). But most of the time during power cut my system turns off immidietly, and upon restarting it shows windows didn't shutdown properly and i know this is bad news.
So i want to know what is d exact reason of it? And i also don't have earthing in my house. Should i get a new smps or a new battrey more powerful?