I was playing an unrelated quest in Morthal when Jorgen was killed by a dragon
attack. One of my next quests will be "Pieces of the Past" and it involves talking
to Jorgen about a quest item. Now that he is dead will I be able to complete the
quest? I know the quest item is in his house, can I still steal it even though he is
dead or will it not advance the quest. I need to know because I can afford to go
back to before he was killed if I have too. I'll just have to kill the Head Vampire
again for the quest I was on.

If you're playing on PC, and don't mind a little "cheating", use the resurrect console code. http://www.uesp.net/wiki/Skyrim:Console#resurrect

If you don't want to do that, you should just save and of course just try it the way you mentioned. Try to see if the item is in his house and if you can get on with the quest, even when you skip the talking to Jorgen part completely.

Maybe just go back to a save prior the dragon eating Jorgen?

Some NPC's are taken to the Hall of Dead in their city when they die. They can have the "quest item" on them as loot. Taking the Item usually starts the quest. If you need specific dialog you might be outta luck...

I looted Jorgen's house key and chest key off of his dead body before I started the
"Pieces of the Past" quest. After I started the quest I went straight to Jorgen's house
and took the quest item form his chest (counts as stealing). I then took the quest
item back to Silus Vesuius in Dawnstar and he took it no problem. So I guess
Jorgen being dead doesn't have an effect on the "Pieces of the Past" quest (So far...).

You should be okay then, he doesn't have anything else to do with the quest.

Thanks.

Well, in my case Silus Vesuius is dead and I can't get back to prior save. What should I do? I really don't wanna start the whole thing over.

If you're on pc, and know where his body is, resurrect him? Otherwise, I think you're stuck....

Nah, you're not stuck even if you've lost the body or it has already disappeared. http://www.uesp.net/wiki/Skyrim:NPCs#Console_IDs happens to cover all your possible needs. Silus' RefID is 000240CE. Enjoy! That is... if you play the game on PC.

Remember the resurrect command is only a 50/50 chance that it will work for a quest NPC or any NPC as Skyrim was coded to respond to NPC's being dead. I have seen it myself a couple times. Here is one example Alvor in Riverwood, in one game I resurrected him and it was business as normal, in another all he does now is sit in his house he does nothing else ever. So save 1st resurrect 2nd

just pick the lock of his house, then pick the lock of the chest.

I can't pick the lock cause it requires a key and I'm playing on PS3.