How did you drape the vectors? I think you need to set the Base Heights. To do so:
- Right click the vector data layer and select Properties.
- Click the Base Heights tab.
- Select the radial button beside Obtain heights for layer from surface. The program automatically selects the DEM open in ArcScene.
- Click Apply, then move to the Extrusion tab.

- Put a check in the box beside Extrude features in layer and change the extrusion value to 2 or 3. Test different values to see the
changes on the map.
- Click Apply to view the changes or OK to return to the ArcScene map window.

Hopefully, that'll do the trick :)
Another option would be to use the Virtual Terrain project. It's an open source 3D visualization tool.
The goal of VTP is to foster the creation of tools for easily
constructing any part of the real world in interactive, 3D digital
form.
This goal will require a synergetic convergence of the fields of CAD,
GIS, visual simulation, surveying and remote sensing. VTP gathers
information and tracks progress in areas such as procedural scene
construction, feature extraction, and rendering algorithms. VTP
writes and supports a set of software tools, including an interactive
runtime environment (VTP Enviro). The tools and their source code are
freely shared to help accelerate the adoption and development of the
necessary technologies.

They have a nice tutorial page. Good luck :)