Copyright is in force until 70 years (95 years in the US, if I remember correctly - this was amended a few years ago) have passed after the year of decease of the creator.
Basicly, as was already noted, this isn't a viable way to look at in projects involving "modern" creations.
However, copyright protects against copying, and "copying" is meant very literally: copy-pasting source code infringes to the right of the copyright holder (very general comment). Using the same ideas and making an another implementation of them does not.
So implementing the idea of a board game as a computer game does not infringe to the copyright of the creator of the board game. (If you make an exact copy of the rules, this would of course be an infringement; or if you make other exact copies , e.g. figures etc. these could be infringing. The ideas are not protected by copyright, so e.g. the same rules can be written differently.)
Besides copyright, one should consider the impact of possible patents and/or trademarks. A board game, or individual parts of it, must be quite difficult to patent (but everything is possible, at least in the US).
As a practical note, if you are going to make a computer implementation of an existing board game following the original ideas very closely, you should expect that the creator of the original idea reacts somehow. Solutions:
1) work together with them or
2) prepare for their reaction.
When agreeing in advance: it is somewhat usual that companies concerned about their copyright protection use clauses in non-disclosure agreements that effectively extend the protection of their copyright in relation to the other party. So if you're going to sign an NDA before negotiations, it might be that your position to negotiate weakens due to clauses contained in the NDA (you cannot anymore use certain ideas without their consent). This depends on the wording of the NDA.
Don't take this as legal advice to you (jon j rambo), as this message isn't. These are general comments relating to copyright. Also, my perspective is European (Finnish).