Day zero I take my laptop out of my room to stream a movie and find out it might as well not have a battery when it hibernates within a minute or two. When I plug it in and power it on, it comes up fine but a bit later it freezes. After a restart it's fine. After the movie, I have it hibernate to move it back. When I power it on, it blue screens, but after restarting it and dumping the hibernated state it comes up fine.
Day one, I use it as normal and have it sleep when I go out. When I get back, it won't wake up. The lights are on (front and button power light, caps lock, num lock, and battery if the battery is charging), but there is no display. I powered it off and when I start it again there is no change. The CD drive does open if I press that button.
I've tried booting with just AC or just battery, without HD and RAM, unplugging and removing battery then holding power (something about discharging static). Nothing changed what happens. I also tried plugging it in to an external monitor, but there was no video there either.
What I find really strange is when it is off, if I plug it in to AC, the fan turns on and the lights come on without me pressing any buttons.
The laptop is an Asus F81SE running Win 7 64 bit. I have it muted and turned off the boot sound, so I can't tell if it just isn't displaying anything. It's ancient but I don't use it enough to justify buying a new one. I contacted Asus, but they "determined the device requires a technician's attention and do not further troubleshoot the issue" but they don't have equipment and parts for EOL equipment.
Is there anything else I can try to fix it?
Update: I replaced the CMOS battery, which stopped it spontaneously turning on when I plug it in. But, it had no change otherwise - still no video (including on HDMI and VGA), num lock and caps lock lights stay on, no activity on a bootable flash drive