There are several different things when dealing with powermanagement issues in Linux.
For instance you have 2 different powermanagement scemes for PC's. APM is advanced power management and ACPI is advanced configuration and power interface.
APM is the older type and is controlled mostly by the system's BIOS. Each Pc manufacturer had slightly different configurations and such.
ACPI is the modern type and it has to do with the computer providing a interface to the OS so that programs in your OS can control the power management.
Some laptops work better with the first sceme, others with the second. Yours probably works best with the second sceme.
Then on top of that there are several different ways a computer can do "sleep".
There are two different ways to get it so that you can basicly unplug everything and store a computer for a while, then power it back up later without worrying about running down the battery so much.
You have the traditional method were the computer remains on, but powers down all your devices and such to preserve power and simply provides enough current to keep information in RAM. Then when you want to use it it powers on all the devices and gets everything running again like normal.
This is the more difficult to get working correctly since all the devices have to be able to be shutdown and turned back on without being reset and without flipping out
The second type is were you shutoff the entire computer, no power whatsoever. The current settings are saved by writing the contents of RAM to your disk, then when you power up your computer copies the information back into RAM and then it's like you never shut it off.
On older APM laptops that supported this feature you had a special partition that held the contents of RAM. So when people formatted for Linux they often deleted this partition and thus lots that features. Remaking the partition fixed it.
On newer laptops (and 90% of computers in general) you can use in Linux something called "software suspend", that is it writes the contents of your RAM to the first aviable swap partition and then when you reboot you boot up like normal and when you get to the bootloader you add or choose a restore selection were the swap partition's name is passed to the kernel as a boot argument. Then it reads the data into RAM and your off and running.
Software suspend is the one that will most reliably wo as it doesn't have to depend on the hardware so much. You can even do things like boot up into another OS or replace power supplies and such so that you don't have to loose your Linux session.
here is some body with slackware on a inspiron laptop.
Links to people's experiances with dell.
http://tuxmobil.org/dell.html
There is decent ACPI support built into the 2.6 kernel, and there is a acpid deamon that helps deal with it. However there are patches that are more state of the art in terms of Linux ACPI support avialbe and documentation on those patches and such is at
http://acpi.sourceforge.net/
There is support for software suspend that most distros build into the kernel, but it's not the latest versions aviable. That support and documentation can be found at
http://softwaresuspend.berlios.de/
Sorry I can't give you specific directions. What options you can use vary quite a bit from hardware to hardware and I can't give specific stuff as I just don't know that much about it.
Software suspend is close to "hibernate" in Windows.
Suspend to RAM is close to "sleep" in Windows.
Dell has a linux specific web resources put together by some pro-linux employees at
linux.dell.com
You can find help with some stuff on Fedora at
fedora.forums
My guess is that Fedora Core3 is new enough that you should be able to get software suspend working without having to patch a kernel and just need to install a couple small packages.