should not the DVD burner's

fault.
what DVD burner does is to write the data file follow the format. the difference should be slow or fast, or write unsuccessful.
Ulead video studio should be fine, what is your version? the current one is 7.0.
The 1.0GHz computer seems slow.
However, I think the settings should be the big concern.

In the Studio, you should select the right format - DVD format. Capture the video first, then make the movie (get the DVD file), don't write on DVD on fly.

after you get the DVD file, play on computer to check how it is, then write on DVD if it is good.