Alright, so I got it working for you! Here are Dropbox links to both the initial exported CSV from MA, as well as the final fixed CSV that imports correctly into DB:
Initial export -- 
dropbox.com/s/dxh021hsj5wz1zd/Inventory%20-%20initial%20export.csv
Fixed for import -- 
dropbox.com/s/11erla8xphy3qwz/Inventory%20-%20fixed%20for%20import.csv
If you attempt to import the initial CSV, you'll find that there are four main sources of the errors:
- Incompatible edition names (82 errors):
- Magic: The Gathering-Conspiracy => Conspiracy (55 errors)
 
- Commander 2013 Edition => Commander 2013 (15 errors)
 
- Magic: The Gathering-Commander => Commander (4 errors)
 
- Planechase 2012 Edition => Planechase 2012 (8 errors)
 
 
- Mismatched card names, which itself was due to 3 sources (28 errors):
- Transform cards from Innistrad, DKA, and SOI had the backside of the cards listed (15 errors)
 
- Split cards, like Turn // Burn, sometimes had only one half named, or had a name like Turn // Burn (Turn) (11 errors)
 
- Flip cards from Kamigawa had the flipped half's name, or had that name in parentheses (like with split cards) (2 errors)
 
 
- Online-only editions (10 errors):
- Masters Edition (1 error)
 
- Masters Edition II (7 errors)
 
- Masters Edition III (1 error)
 
- Vintage Masters (1 error)
 
 
- Æ character in card names (7 errors)
 
I fixed the edition names and changed Æther to Aether.
As far as the online-only sets, Deckbox does not (and far as I'm aware doesn't plan to) support MTGO or Arena (since a primary feature of Deckbox is trading paper cards). I went ahead and kept those cards at the end of the fixed file, just for your reference. I had to move the counts of each card to an unused column (so Deckbox will ignore them during import).
Finally, I recommend double-checking your physical inventory against the database when it comes to the split, flip, and transform cards. It feels like your Deckbox inventory may now have duplicates, because I believe that MA was counting each half / side of those cards as individual cards. I did keep the alleged duplicates in the fixed file, as separate rows, but I noticed that they always had the exact same count. For instance, you'll see two rows for 4x Delver of Secrets. This will show a total of 8 on Deckbox, but my bet is you own only 4?