The reverb on my Twin Reverb Reissue stopped working yesterday right while I was playing.
... when reverb and vibrato are on at the same time the amp makes a noise resembling the one of a helicopter. ...
Are you the original owner? Is the amp still under warranty? If so, I'd take it to the music store and have it fixed on Fender's dime.
If I bang on the amp, I can hear reverb, so I suppose V4 is working.
If that happens, everything from the reverb tank springs to V4 output is fine.
There might be a break between C13 (500pF) and the reverb tank springs, or there could be another issue. For reference, the schematic and layout of the Twin Reverb reissue are
here.
Do the voltages seem ok ?
All voltages are fine. The 0.1mV are probably
really 0vdc; eithe way, they are close enough we'll call those 0v.
I notice CP28-31 are connectors from the reverb send circuit to parts off the p.c. board., including connections to the reverb transformer and the reverb send jack. If any of those are loose or making intermittent contact, you'll have problems with your reverb. Have you checked to make sue these are in place and tight?
... It's also worth mentioning that when reverb and vibrato are on at the same time the amp makes a noise resembling the one of a helicopter. When the reverb is off, tremolo works perfectly. ...
Helicopter sound not made by the trem?

Just kidding. Both of these circuits share a filter cap, so they could influence each other. But that cap is also used by the output tube screens, so it seems unlikely it's bad. At the power end of the board ae connectors for the "Z" filter cap and its ground (CP24, CP25, CP18). Each of those should be on and tight.
But really, you ought to have a Fender service center be responsible for Fender fixing it if there's any chance it's still under warranty. It's possible there is a tricky fault you're not prepared to troubleshoot (meaning a test signal and an o'scope or speaker would tell you if everything is good up to the output of the reverb transformer).