Shouldn't be a problem as long as the motheboard BIOS can cope with the new CPU. If it can't, then flash it to a newer version BEFORE the change
The E1400 and E3400 are both dual core, so you shouldn't need to have to worry about changing the HAL from single to multicore
I question the point of the upgrade though - you're going from a 2Ghz Celeron to a 2.6Ghz Celeron. OK, the onboard cache is doubled, and the CPU uses a 45nm rather than 65nm architecture, but I wouldn't have thought the upgrade warranted the hassle. And you may have problems finding one anyway - socket 775 is a dead form factor. A quich search of my usual suppliers finds NO 775 Celerons available
Some dealers still have socket 775 Core2 quads available - you'd be better off getting one of those, especially if you mean to keep the machine for a while