Colt 1903 Hammerless - Will it fire?

I found this rusty Colt Model 1903 Hammerless at an auction. The outside is completely pitted, but inside it doesn't look so bad. Is there anything preventing it from firing?

DISCLAIMER
All subjects featured on this channel are shown for historical and informational purposes only. All gunsmithing work is intended to restore the item to it's original condition, never modifying to serve any other purpose. In no way, shape or form is anything featured on this channel ever intended to be sold at any time. Any messages regarding selling a firearm, ammunition or an accessory will be removed. Everything shown is legal where the creator is located, please check your local laws.

00:00 Intro
02:48 Field stripping & Inspection
05:01 Disassembly
05:44 Fixing the trigger
08:14 Reassembly
11:33 Shooting
13:34 Conclusion