I am appending to this ancient thread because it's the first hit on Google for "hibernation tab missing", and I wanted to give some more info on what's wrong.
Step Zero! Open the command prompt, type "powercfg /a". It'll list things you can do and it might simply tell you what's wrong. "powercfg /hibernate on" will enable hibernation, or give you an error. For some reason most pages don't mention this utility. I have no idea why.
To actually fix things, first check to make sure there's no yellow exclamation points in your hardware manager. That will kill you instantly. Install all the appropriate drivers. Update old ones. Make sure you've got the recent chipset driver, because, if you don't, you fail. (And will be terminated.)
Second, head back into that hardware manager and click the "computer" thing to open it up. Nowadays, your computer *should* be ACPI. It might be APM, which will probably still work. If it's "standard" then something went wrong, update your BIOS and/or reinstall Windows, it just shouldn't say this. "Standard" is hilariously obsolete.
Now, the part that always stumped me! If you tried the powercfg thing and got a message about PAE mode, you might have 4 gigs or more of RAM. If you have well over 4, sorry, you're just going to get anywhere, ever, as near as I can tell. Give up, go home. Microsoft has decided that people with more than 4 gigabytes of RAM are not allowed to hibernate because it would be too slow. I am honestly not kidding here.
If you have 4 or less things get a bit tricky.
There's some strange interaction between PAE, the NX bit, the 4gb limit, and XP 64 (possibly Vista 64 also.) I am not sure what exactly. I've encountered sites that say NX is mandatory with XP 64, and therefore PAE is also, and therefore hibernation never works, but I've gotten hibernation working so obviously that's just false.
Going into boot.ini and adding the /nopae flag will attempt to disable PAE. Adding the /execute flag will attempt to disable NX. (You might already have a /noexecute flag - you'd obviously have to remove it.) However, if you have 4gb of RAM, you might have to do what I did, which is add /maxmem=4032.
Good news: it might work after you do this (you might not need to do /nopae or /execute or anything either.) Bad news: it might cut off far more RAM than you really want. My 4gb system is down to 3.5gb after doing this.
But apparently it's the only way to make this work.
I should also mention that if you look around enough you'll find references to a utility called "apmstat.exe" that's supposed to help, but it doesn't work on ACPI computers and most computers are ACPI now. So if you have an APM computer, go hunting down info on that if you like, but I can't help you with it and if your computer is ACPI it just won't do anything (it will yell at you for trying.)
So there's Zorba's Bucket o' Tricks. Hope this helps someone besides me.