I recently just got my first MacBook Air. I already have an iPad mini and I just changed my Apple ID. I had everything set up before I decided to change it and iMessage was working perfectly on both devices. Anyway so after I went through all the hassle of changing my Apple ID when I went back onto my laptop, it won't even let me send a message even though I have set to my new Apple ID.
The vast majority of the time when iMessage no longer delivers to a Mac (or iOS device) is due to the time settings where the clock has drifted.
I would work through this checklist as you rule out any account related issues (especially the part about appleid.apple.com to verify the account isn't locked):
It also covers a big reason why messages fail to be delivered even if you can sign in - firewall settings and networking issues between the Mac and the APNS servers that alert your computer a message is coming and help deliver the message itself.