There's a simple way of running "The Need for Speed SE" in DOSBox with working in-game videos,
without having to use svga_et4000 and UNIVBE.

First of all, the fix IS NOT by me, I got it from a blog 2-3 years ago.
Can't remember the name of the site, though.

Apparently, NFS.EXE has two modes for in-game videos.
A lower quality one (8 bit colour iirc) and a higher quality one.
The higher quality one IS BROKEN. This isn't an issue with DOSBox, it was coded that way.
(According to the blog, no videocard used the higher quality mode back then,
so the fault wasn't discovered or fixed).

To fix this, NFS.EXE has to be forced to use the lower quality mode by default.

1. Back up NFS.EXE
2. Open NFS.EXE in a Hex editor
3. scroll to line 000607E0
4. change the value of the seventh set of data (offset 607E6) from 00 to 08

the line should now look like this:

E8 DD 67 08 00 6A 08 68 C8 00 00 00 68 40 01 00

5. Save the file

That's it. Now in-game videos should work with the default s3 videocard in DOSBox.