If you're experiencing software issues, restoring WITH backup properly won't fix your problem. Therefore I always recommend that you set it up as new, to get a clean install. Kinda like what you would do with a Windows computer.
I appologize for the lengthy read....I just wanted to be as thorough as possible. I am not a noob at this so this is really kicking my ass. I can solve most issues with jailbreaking and unlocks, but damn this DFU mode is a bitch.
I am having the exact same problem with my iphone 4. I will start from the top.
I just bought an iPhone 4 on August 6, 2011. I am currently still using my iPhone 3gs until i get the Gevey unlock sim off ebay i ordered (hopefully mid this coming week). Couldnt pass up a practically brand new iphone 4 for 400 bucks. Anywho.
Came with 4.3.3 firmware on it baseband 04.10.01.
Sycned it with my itunes but some things were acting screwy since it was already jailbroken i decided to do a restore. It had shsh blobs saved on Cydia 4.3.3, 4.3.4 and 4.3.5. So i knew i could just stay at 4.3.3. So i put it in pwned DFU mode with pwnagetool, used TinyUmbrella's TSS Server and Restored multiple times with 1013 error and kicking straight back into DFU mode this whole time mind you. After combing the internet's iDevice forums i finally came across one that told me to check the UPDATE BASEBAND option in tinyumbrella. I had seen that option under advanced before after going into that window about a 10 different times changing crap.
As this is my first iPhone 4 i was not too sure what the latest baseband was so i did some research and found out that it was ok for me check that as the baseband has not changed from 4.3.3-4.3.5 just the jailbreak has. So i checked it. BAM was able to get itunes to restore without the 1013 error.
But now i was still stuck in DFU Mode loop. not recovery loop, that is one thing i have found is a lot of these forums were talking about recovery mode loop (connect to itunes icon) which i never even got once. Which did not help my case.
So i tried to use FIXrecovery43 the file not the one in Tiny umbrella (that one doesnt do crap but get stuck at the greenpois0n menu on my iphone). And it goes through its whole process like its gonna work and nothing right back into DFU mode again. I must have done this at least 10 different times. Every time back into dfu mode.
I tried installing cydia with Redsn0w which went through the whole jailbreak process a couple times, but right back into DFU mode, and 2 other times i tried this it stuck on the running pineapple Activating Bundles (i think thats what it was) either way whenever it was finished it would eventually go back to DFU mode.
Got sick of that so i tried boot tethered for now on redsn0w and what do you know it booted in just fine and now my iphone works. But i have to treat it like a tethered jailbreak but a little different, this one just goes back into DFU mode if i reboot or shut it off. Its really strange and quite annoying.
Oh forgot to mention i just updated to 4.3.5 and it worked just fine with an official apple update. Was able to downgrade back to 4.3.3 without any itunes error but guess what my good old friend DFU mode.
So its not any software issue, my firmware is just fine and runs great as of right now. its still syncing and i restored from NEW iPhone.
As of right now, just DFU Boot loop if i reboot it or shut it down and just use it like a tethered jailbreak, but there has to be a solution for this. Unless an untethered jailbreak comes out for 4.3.5 i am just gonna be using Redsn0w to boot it up.
If anyone has any insight or would like me to elaborate more about something, i am all ears. Sorry for the long post but i have literally been working on this all day and i sill did not explain everything i did to a T.
Thanks in advance.