I got the INQ from Koodo today, had it activated in store, and it worked.
About 10 minutes later the phone got crazy laggy, nothing would work, and the phone kept turning off and on..

No idea what's going on, but it's my first phone and it's pretty shitty because it's a nice phone and it won't work..

If anyone has any helpful suggestions I will donate some FG for the working solution!

Take it back to the store and tell them. Duh.

Faulty battery perhaps? Turn the phone off, fully charge it, then try it from there.

On my INQ, I had to stop the "e-mail by 3" service, because that ate A LOT of power and the phone would heat up instantly, and just caused a mess. If you disable that, you should be fine. I don't remember having a problem like you did, but it was pretty annoying having a battery life of 30 minutes.

Sorry if this doesn't help, don't know what to suggest. If you can't get it working for a while after that, contact the store.