If I think my liquid yeast was not viable yet pitched it unknowingly and now no fermentation happening-can I introduce new yeast or trash the batch ?
Sure, there is no problem pitching additional yeast. How long has it been since you pitched the yeast and what was the expiration date on the package. If yeast gets near the expiration date a lot of the yeast cells have died off and it may take longer for you to see actual fermentation activity, sometimes up to 18 - 24 hours. The yeast may be actively reproducing during that time but you would not see any signs of fermentation. I always suggest making a yeast starter so you know you are pitching an active culture and the proper amount of yeast cells for the beer you are making. t
Feel free to add more yeast, it won't hurt. If you add a different strain of yeast it may affect the final flavour profile. It usually takes about a day for the initial signs of fermentation to appear if you haven't made a starter.
Only trash the batch if you are certain it has become contaminated, this would only become apparent after a few days.
I would always suggest making a starter with any yeast you have old or not, dry or liquid. This ensures that the yeast you pitch is healthy and ready to convert all your wart into delicious beer. Here is a little intro: https://www.youtube.com/watch?v=jMhFerNTwbQ