A Celeron from 2006 and no add-on video card will not run Minecraft. It will stuggle alot with it even with a video card.
You need to get a new computer.
A 3 gig Core 2 Duo or a Core 2 Quad would do it along with a lower end gamig card like a Radeon 7750 which you can find used now, and is a good card for lower power systems.