It is possible to change IMEI on K750 with more tools, cables, software...
Yes, it is illegal to change it in some countries but sometimes after some service actions (repair, change parts and more reasons..) we have to change IMEI. And this action is not illegal if we write IMEI of this phone not any other. And whitch IMEI you mean to write into your phone? Maybe you will write IMEI from somebodys phone and then his and your IMEI will be blocked?

Before correct answer i have some questions for you:
Where you are (country) becouse in my area any phone has not blocked IMEI?
What do you have for K750? Any software, tool, cable?
What happened when you try to make a call or send SMS? What you see on LCD or hear?
And make one test:
Turn on speakers on PC. After, turn on K750. Do you hear loud noises?
If Yes, now try to call. What about noises now? Maybe your K750 have problems with antenna, battery, software or something else?

Help me to help you.