Have you checked the vacuam line to the shut off valve on the injection pump? It is somewhat common for it to get knocked loose when changing the oil filter. You can also use a vacuam guage to ensure that it is getting vacuam to shut it off.
The cold start problem may very well be the glow plugs. An '83 has pin type glow plugs and I have had to replace them every year or two. Even if they are still making continuity, they will still sometimes need replacing, and I live in Texas. The temperature sometimes gets into the twenties, rarely lower. If you are in a cooler climate, it proabably presents even more of a problem. Just to make sure that the relay is okay, you can connect a voltmeter to one of the plugs when cold, turn on the key and ensure that it is getting voltage.
'84 Euro 240D, 516K miles
'88 300E 5 Speed
Over 800,000 miles in