If I fail a spell check to gain a combat check bonus, am I unable to equip another item?
That hand is used up for the combat round.  Next round you may equip other items/spells with that hand.

This is covered in the FAQ.


  Q: During combat, how long does a failed attempt to cast
  a spell use up an investigator’s available hand(s)?
  
  A: A failed attempt to cast a spell uses the specified number
  of hands for an entire round of combat (i.e., for one
  iteration of combat steps 2 and 3.). In subsequent rounds
  of combat, the investigator may switch to a new weapon
  or try to cast a different spell.