How long would the 100 Year Cryptography Project have secured its data had it been started 100 years ago? The goal of the Tahoe-LAFS 100 Year Cryptography project is to "enhance Tahoe-LAFS's cryptographic system so that Tahoe shipped today/next year might remain safe from cryptographic attacks for a 100 years."  Its developers are openly collaborating knowledgeable experts in the field, with at least all the information on the internet today at their disposal.

How long would such a project have secured its data had it been started 100 years ago?

Is the length of the secure period monotonically increasing as we ask the question with starting points less distant in the past?
In 1911, there was no computer either. With much more modest goals of security for the next few months, the German army came up with the Enigma, which was broken. Before the 1970s, cryptography was essentially a military-only domain, so there were no "openly collaborating knowledgeable experts". The situation was qualitatively different. So it is a bit unfair, and of limited scientific value, to try to compare cryptographic systems before and after the seventies.

Moore's law was published by Gordon Moore in 1965, and thus was quite well known 10 years later. In 1976, people trying to build a system which would still be safe 100 years later would have accounted for Moore's law, meaning an extra 100 bits for symmetric keys, and 200 bits for hash functions (there are several variants of Moore's law, but one of the most optimistic says that every two years you can put twice as many transistors on a given die and clock them twice faster, leading to a doubling of CPU power every year). Symmetric encryption was beginning to be understood; DES had just been approved as a US standard, so, presumably, people aiming for 100-year security would have proposed something like 5-DES. They might have missed the point about block size: DES has 64-bit blocks, making it unsuitable for securely encrypting more than a few dozen gigabytes with a given key. Even if believing Moore's law, the sheer volume of today's data was not envisioned at that time.

In 1976, there was no hash function worth speaking of. The Merkle-Damgård construction was published in 1978. Even MD2 did not appear until 1989.

Digital signatures may have been a problem. In 1976 there was no efficient digital signature system. When RSA was published in 1978, the article contained an overly optimistic comment about how a 512-bit integer would resist attacks for millions of years (this became breakable in 1999). Also, appropriate padding techniques were not developed until the early 1990s.

So a "100-year cryptographic system" developed in 1976 would have been partially broken by now; but some parts would have kept well (probably symmetric encryption). Also, the system would have become inadequate for our evolving needs, in the same way that even a very fast Enigma machine would still encrypt characters out of a very small set (only letters, no space and no digits !), making it unsuitable for encrypting bytes.

This shows that we tend to get wrong ideas about what the future will hold (we are in 2011, where is my flying car ?). In particular, we do not understand what we will need 40 years from now, and we have relatively little grasp of the threats that will appear at that time. Right now, the trendy fearsome threat is the Quantum Computer.

(This is all an intricate way of saying that your question cannot be answered.)