The one with the ThunderBolt is likely to be a ThunderBolt "Pro" cable. Any full-speed ThunderBolt cable over a half-meter requires it be an ACTIVE cable, that has signal re-drivers in it. If you bought a new one of those from Apple, they charge US$129.
That you can get something from HDMI suggests the display may be working.
The ThunderBolt INPUT port is the one next to the audio jack, in the middle of all the jacks, near the HDMI ports. The one at the end is a USB output.
to get a Mac display to become active, you need the Mac to query the display, and the display to answer with its name and capabilities. Otherwise, the display will not be shown as present, and no data will be sent to the display. "No signal detected" is generated by the DISPLAY, not by the Mac.
This query is only sent at certain times:
• at startup
• at wake from sleep — so momentarily sleeping and waking your Mac may work
• at insertion of the Mac-end of the display-cable, provided everything on that cable is ready-to-go
• on invoking Option-(Detect Display) button in Displays preferences (from another display)
so try doing some of those things and see if the display comes alive.