You need to use a conditional operator. The logic is:
Result = If {new DEM has values, use them}
Else {use values from the original DEM}.
Alternatively, this can be expressed as
Result = If {new DEM does not have values, use original DEM}
Else {use the new DEM}.
In ArcView the syntax varies with the version: there's one syntax for versions through 3.3, another through 9.3, and a new syntax in 10.0. (No doubt the syntax will continue to change every few years, which is why it's so important to reason about GIS in a software-independent way.) The alternative expression is simpler in ArcView. Its 9.3 syntax looks like
CON( IsNull([New DEM]), [DEM], [New DEM] )
More generally, suppose the new DEM includes some values you don't want to use, but you have another grid--representing your polygon--indicating where you want the new DEM to replace the old. Let's call this polygon grid "I". This variant would be expressed like
CON( IsNull([I]), [DEM], [New DEM] )
As you can see, the procedure is quite general: you have a "base" grid (the original DEM), a new grid containing values you want to "patch" over the base grid, and a "zone" grid indicating where the patching should be. A conditional expression implements grid patching. This approach will let you patch grids in any raster-based GIS that supports map algebra.