Springs are only found in spring reverb units eg 'Accutronic' reverbs. Old delay units used recording tape (eg WEM Copycat). The delay section in your V'x is entirely digital.
I'm assuming we're talking about purely the amp on its own with no floorcontroller connected.
Are the LED on and do they move between each delay option when you press the button. If no LED is lit then it's possible the problem is 'mechanical' and the delay 'type' button has got stuck in the off position due to dirt/oxidisation. Try spraying a little electrical switch cleaner around the sides of the button and pressing it repeatedly to see if the switch connection can be made.
If not, it's a software problem, or your amp has developed an internal mechanical fault, which will need diagnosis by an amp tech. You've already tried a reboot, but if cleaning doesn't work, try a reboot 2-3 times more as it may not always fix a filepath corruption first time round.
If you can't fix it yourself, talk to Vox technical service to see what they suggest.
"I started out with nothing ...and I've still got most of it left!" (Seasick Steve)