Like Sutek said -- if you're already using houserules, then really it's your call.
The 'official' ruling is that there's no rule in the core book that says a disarmed bloodlusting psychopath does not have the presence of mind to pick his weapon up. As a matter of fact, it seems very reasonable. Even in a blind rage, you'd have the presence of mind to grab the most dangerous thing in the room.
The only rule I'd enforce here would be that the barbarian must pick up the weapon -closest- to him, so it won't necessarily be -his- weapon that he picks up. Further, I'd probably say there's a flat 50% chance that if a non-weapon is right next to his weapon, like a rock or a chair, he picks that up instead.
If you want precedent - I can think of two examples off-hand.
The first is Conan. The quintessential murderous psychopath. I don't recall a time when Conan simply ignored any and all weapons to bash someone in with his fists. Even in his rampages, Conan was intelligent enough, and had enough presence of mind, to pick up weapons, or even retreat.
Another good precedent is Achilles -- I'm sure you're familiar with him. He was said to go into a murderous frenzy during combat. But he still had the presence of mind to throw multiple spears and draw a sword when his spears were spent.
Nothing about the various d20 Fury/Frenzy/Bloodlust/etc abilities ever say that 'rampaging' means 'stupid, brutish, and completely without sense.'