You are knocking on the wrong door, what you need is a service, a programmer could do what you are looking for in exchange of a fee.
Btw, you can't reproduce the exact conditions of when your private key was generated, the purpose of randomly generated key is to avoid reproducing it again.
I suggest to open a service request here https://bitcointalk.org/index.php?board=52.0
And ask for a willing programmer, you will see how fast you get what you need.
Good luck, hope you find your coins.
This is a 120 bit private key with the remaining part all zeros: 5HpHagT65TZzG1PH3CSu63k8EXXXXXXXXXXXXXXXXXXXXXCggk4
This number of bits have been solved in the infamous puzzle challenge, but with great computational effort.
The address is 1HCQXqpBwLpwWQ2F2995PwcAPVkTdtpAHe - I've now used it in four transactions so that gives you four signatures. Feel free to claim it. I will in addition give you 0.03 BTC if you give a full explanation with code after claiming it.
It's not really "gold" since it's such a special situation, where over half of the bits of the private key is known. Just curious if someone manages to find a way where multiple transactions (with proper nonces) actually weakens the security of such a key.
You know what? Now that I think about it, puzzle 120 and 125 both have 2 outputs, they never revealed the keys, if somehow some anonymous individual claimed the few bucks on your address and at the same time revealed the keys for 120 and 125 but without revealing any algorithm/ program, it would be really great, ! Right?