There were a boatload of iBook variants in 2002. Find the serial number. If it is not on the outside, look in the battery bay. Enter the serial number in this page to find the exact sub-model:
https://everymac.com/ultimate-mac-lookup/
I've used that site many times and find it safe. Please tell us what that shows for the sub-model including screen size, BUT do not post any serial numbers here.
A couple of thoughts:
— During the early to mid 2000s, some Macs had display failures that proved to be manufacturing defects. All computers affected had serial numbers starting with the factory code W8. Most were iMacs but there were some laptops affected as well. Today, that is unrecoverable.
— This: " It hasn't been turned on for 15 years." Any device that sat that long may have a litany of issues.
1 — A "PRAM" battery or a backup capacitor supply a bit of power to maintain user settings when no power is getting to the computer. Some Macs of that vintage would not start in the presence of a dead PRAM battery or a drained backup capacitor if the main battery was dead or missing. Others might show issues like a dead display. I do not see a PRAM battery listed in repair sites for the iBook series so I am guessing it is capacitor-based
The old "bush fix" we used in the late Cretaceous was to leave the computer attached to wall power with the battery removed and power off for about 24-48 hours, then see if you get a normal boot and usable display.
2 — Crud check. Before I attempt to start a computer that has been idle a long time I do a few checks:
a — remove and reseat RAM modules several times to clear any oxidation that has "grown" on the contacts.
b — if the fan blades are visible, I give them a nudge to make sure the fan motor is not seized.
c — specific to your symptoms, you may want to find where the display cable attaches to the logic board. If you can do so safely and the cable is socketed to the board, gently undo the cable and reattach. That's for the same reason as removing and reseating RAM modules
We cannot post links to non-Apple repair sites here. but a search for "ibook take-apart" should guide you in finding illustrated help for removing the the RAM and the display connector.
3 — If you have a bootable optical disk, like an Apple install/restore disk, try booting from that by pressing and holding c when booting. A successful boot from an optical disk could overcome several things but here I'm recommending it to see if the issue is your ancient mechanical hard drive. 2.5-inch laptop drives, regardless of what make of computer they serve, are not as robust as their bigger desktop-class siblings.
Were I a physician, my prognosis for this computer that I can neither see nor remotely access would have to be "very guarded," but let's not send for the hearse just yet.