Our company has been purchased --- we have been advised that our existing 401k program will go dormant and be managed by a trustee of the takeover company.
Under the takeover any new contributions will go into a new 401k fund within the takeover company. Is there a way for a employee to gain control of the funds in the dormant account. Can a written request be made to the IRS? What would be the process to have the dormant account funds placed into a self directed IRA account.

If the plan followed the employees to the acquiring company, then probably not - you need a distributable event to have distributions, and as long as the former employer doesn't retain control of the plan, one does not appear to exist. You should still; however, have the same rights and features in the dormant plan as you have had previously, and the assets clearly must be invested (whether by participant direction or by the trustee). It is possible to merge the plans, if the new employer wishes to do so.... There may be liability issues if the old plan had any problems in doing so.