First this is a link free discussion as spammers pile on to this sort of question.
Next you can google that question and I see it's a common question with plenty of discussions. However to get the PERFECT FIT is not so easy since you have higher requirements.
Your IT staff or web master at the moment should be grilled over their lack of how to google or code. To me this is a gross neglect of servicing you. You may want to just fire them.
I am looking for a live chat software which perfect fit for my WordPress Ecommerce website. I need little more features like one should be connected with woocommerce plugin and I can mark my customers with their purchasing history and order IDs so that We can easily communicate with customers. I have searched quite a few live chat softwares like Cugic, LiveChatinc, PureChat, and now confuse which one would be more ideal for me. If anyone has experienced them so kindly share your experience here.