Diagnosis
It's almost never the remote itself that's broken. The first thing to check is the battery, but the second, more common issue is the remote's IR signal not reaching the projector's sensor.
How to Fix It
1) Replace the remote's battery (it uses a CR2025 coin cell). The battery that comes with it is often weak. 2) Point the remote directly at the front of the projector, specifically at the little dark IR sensor window near the lens. 3) Make sure there's no bright light (especially from the projector lamp itself) shining onto that sensor, as it can drown out the signal.
If That Didn't Work
The projector has physical buttons on the top. Use the power button there to turn it on. If the buttons on the projector itself work, then you know the issue is 100% with the remote or the communication between them.
Heads Up
The remote is very basic and has no pairing or sync function. It's "dumb" infrared. If a new battery and a direct line of sight don't fix it, then yes, you'll need a replacement universal IR projector remote or to rely on the top buttons.