Seems most likely that the lack of sse2 support for the CPU is the cause of the problem (as per signum and PeterT).
I searched for earlier threads and found these:
In particular posts 10 & 11 of the 2nd link. Not sure if a workaround is possible. May have to upgrade my computer if I want to run Sigil.
It would have been helpful if this issue was mentioned in the installation instructions of the Sigil wiki.
BTW. Bought the computer in 12/2003.