i had same problem - turned out my character diddent have anything in inventory and hence the equip button was deactivated - when i bought one item the equipment button worked agasin

Verifying that I've seen the same problem.  The button only works after you've added something to the inventory for that hero/sovereign (via shop, ruins, trading, or combat).

For now, the workaround I use is to click on the character portrait, then click on the 'equip' button or whatever it is in the character info card.  That'll get you to the inventory. 

This becomes necessary as I like to know what equipment I have on hand before entering the shop and end up buying something that hero already has.