Unfortunately there were too many changes made between the original release of D2:ED and DKS to maintain saved game compatibility (ie changes to enemy experience and placement, additional sets and unique items added and some of the D2:ED set pieces moved, changes to skills and enchantments, etc). Since D2:DC is essentially DKS with an added (optional) Developer Mode cheat window, it can not load original saves either.
If you buy the add-on Flames of Vengeance you would be able to install it, load your save at the end of D2:ED and continue with the same character.
As Artki said, though, in D2:DC you can start a new level 35 character at the beginning of the add-on section of the game, and re-create your character. You wouldn't have the same equipment, etc, but you would likely be upgrading that relatively soon, anyway.
With the PC version of D2:ED (or FoV/DKS) you may be able to get a free upgrade to D2:DC from the
Larian Vault; see
here for details.