Please check out http://support.smartbear.com/viewarticle/42533/ for information on support for Chrome 42 and NPAPI plugin. TestComplete works with Chrome 42 with the changes outlined in the article mentioned.
SmartBear supplies patches for each version of Chrome: http://support.smartbear.com/downloads/testcomplete/chrome-patches/
When Chrome gets to version 45 I would assume SmartBear will roll out their NPAPI replacement. But that would be a question for SmartBear support.
If I read your message correctly you say that keyword tests worked in IE but now your tests are not working. Perhaps you can post for some help with that issue?
No, my tests never worked in IE. And I just diappointed that Chrome may be unsupported browser. I hope SmartBear will replace NPAPI to PPAPI plugin.
