IF one of the glow plugs are broken, the glow plug light will remain on while the engine is running, along with the check engine light. There is an easy way to see if the glow plugs are drawing any current but it's too risky explaining it. Gotta be shown rather than written.

Since you stated previously that the engines stumbles while starting I would asume that one of the glow plugs arent' working. Recently had the same issue with our '99 stumbling and then the glow plug light stayed on so it was obvious it was a glow issue. After replacing the glow plugs she started right up, although the check engine did last a few days or so and went away on it's own...

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'97 E300
'99 E300