Help with a dying Palm.

[RDGlenn]

I'm not sure if this is the right place to ask this question, but I
recently purchased a 6' and 8' indoor palm plant that is quickly dying on
me.  I'm not sure what specimen it is, but it is a single trunk with 5 to
6 fronds.  The smaller fronds are turning yellow and brown and dying--and
the larger fronds are now doing the same thing.  I water them once a week,
they receive indirect sunlight for approximately 4 hours per day and I
keep the windows open whenever possible for ventilation.  I even tried
talking to it, but that doesn't seem to help.  The average temperature in
the house is around 68 to 70 degrees.  What can I do to save them?