It's not only a "you're screwed" system it's a "if you don't know what you're doing with this, it's not our responsibility to bail you out" deal too. EFS is actually not meant to be used in a one-off environment like yours. It's meant to be run in a managed environment with a PKI or and Active Directory server to escrow the certificates. At the very least it's meant to be used on systems that had DRA's specified.
Software making skills have very little to do with decryption either at this point. The best software in the world can only try and churn numbers through the RSA algorithm and then do an inspection of the results applied to an encrypted file. The RSA algorithm, while not the absolute best there is, is suffeciently good that unless you have a massive amount of computing power behind you. Some software is more intelligent at which exceptionally large prime numbers to try factoring, but you're still dealing with bruteforcing massive files to try and find the key.
EFS can be cracked given various windows system files such as the Private and Master Key Containers. THose are typically protected with a pretty standard hash of the user's login credentials. But without any of the files associated with EFS, or any encryption system you only have blocks of garbled data.
Garbled data, without any of the "clues" from those above mentioned filed, can only be brute forced. A brute force attack on an encrypted file is to try pumping in randomized (but valid) keys. In this case 1024-bit RSA keys. An RSA key can be generated using the math on this page:
http://www.di-mgt.com.au/rsa_alg.html
Really, it's in guessing the right prime number, and then guessing the right seed for the equation. But there are a lot of prime numbers out there, and the really really large ones which are used in encryption algorithms take a long time to push through any formula. But on top of trying every combination, some inspection of the results of each attempt is needed. Which is why decrypting large files (anything longer than a few lines) is extremely difficult and takes a massive amount of computing power.
To give you an idea of the time involved for mortal machines in brute-force cracking, distributed.net runs projects where thousands of PCs around the world work together trying every potential key combination on a simple one sentence text file. They are currently working on a 72-bit RSA encrypted file. They've been working on it for 1,345 days now at a total rate of 139,000,305,844 keys attempted per second. Roughly 7,013 computers were working the problem yesterday and they managed were able to crunch 11,297,795,508,011,007 keys, or roughly 0.000239% of the total number of potential keys. It will take an estimated 416,560 days or 1,141 years to check the entire keyspace.
Now, imagine a key many million times stronger than a 72-bit key. (1024 is 7 million times stronger than a 512-bit key for example). How long would it take to brute force that given the 7,013 machines globally that were working on a single line of text yesterday?
WinEFS is actually certified for government use (though they use the stronger 3DES algorithm). It wouldn't be if there was a privately held backdoor, or even a master key. EFS uses the publicly tested and time proven RSA algorithm, which has no found vulnerabilities to date. EFS encrypted files stand up to encryption standards scrutiny, so as a raw file they're virtually impossible to decode.
Your only hope is that there are some files that survived your windows wipe through some miracle. Otherwise you're dealing with an honest-to-god mathematical impossibility.
EFS is weak so long as you still have the original Windows setup of the machine that encrypted the file. Without that, it's as strong as any 1024-bit RSA encrypted file out there.
