Wake on Lan WOL - static public IP

Hi,
please help, I have one older computer with static public IP from provider. Everything is set, from BIOS, from OS. From command prompt I found out that everything I need is running and that I'm not behind any router to check out ARP settings. My IP is static and public but after few seconds, it's not more than one minute, I am not able to wake that PC up. This is main issue in my point of view. On many threads all across the web I found many users which WOL forking only 5-10 minutes after shut down. Mine is working one minute maximum. And second on this is that I'm not able to set ARP because I'm not behind any router. In this case, isn't WOL supposed to work with BIOS and OS settings? Or is ARP an issue for static public IP too?
Thanks, I'm here online and already done a lot of research on that. If I can post something for better suport maybe I've already done that so please.
PS: Maybe BIOS upgrade? There is some WOL settings but not very clear.

Well, before we get to the point where we might offer help, finish getting us some system specs on teh machine you're working with.

System Specs

CPU: Intel Celeron D 356 (Cedar Mill-V, C1)
3333 MHz (25.00x133.3) @ 3345 MHz (25.00x133.8)
Motherboard: ASUS P5GPL
Chipset: Intel 915PL (Grantsdale-PL) + ICH6
Memory: 1536 MBytes @ 200 MHz, 3.0-4-4-8
- 1024 MB PC3200 DDR-SDRAM - Kingston K
- 512 MB PC3200 DDR-SDRAM - Nanya Technology M1U51264DS8HC3G-5T
Graphics: GIGABYTE GV-NX62TC
NVIDIA GeForce 6200 TurboCache, 128 MB DDR2 SDRAM
Drive: ST3160815A, 156.3 GB, E-IDE (ATA-7)
Drive: ST3160815AS, 156.3 GB, Serial ATA 1.5Gb/s
Drive: HL-DT-ST DVD-RAM GSA-H22N, DVD+R DL
Sound: Intel 82801FB ICH6 - High Definition Audio [C0]
Network: Marvell Yukon 88E8053 PCI-E Gigabit Ethernet Adapter