RE: Dell D810 Laptop Suspend/Resume

S3 is suspend to RAM (MS calls it standby, IIR)
S4 is suspend to disk (MS calls it hibernate)

you can enter either state directly via
# echo 3 > /proc/acpi/sleep
# echo 4 > /proc/acpi/sleep

or equivalently

# echo mem > /sys/power/state
# echo disk > /sys/power state

cheers,
-Len