Sorry dudes, but there isn't a way to sort out the problem as of yet. Personally, I think it's due to some graphics cards being "too modern". When I reformatted my PC, populoud the beginning worked fine until I reinstalled my current graphics card, which is much better than the integrated one I have.
Here's a quote from the "sold out" website giving their answer:
A: This is a known problem that is caused by an incompatibility issue with your SiS Mirage 3 integrated graphics. At this point in time there is no fix for this, but we are hoping to address a patch that will solve this some time in the future. In the meantime, we can exchange your version of Theme Hospital for an alternative title of equivalent value from our product range if you wish. Otherwise, we can only recommend you upgrade you graphics to a non-integrated solution, you try and return the product to its place of purchase or else try playing the game on an alternative system.
Like I said, they think it's integration, I think it's overpoweredness.