Laptop turns on, no image, fan goes off after 5sec

Please, I'll really appreciate you guys helping me with this:

One of my old laptops had a faulty battery for a long time; normally I just reset it and then it ran ok for awhile but today this didn't help.

After resetting the battery, laptop won't turn on, led goes on, fan goes on but turns off after about 5 secs, it doesn't show any kind of image not even bios.

I opened it up, disconnected the battery, reconnected but it didn't help at all.

Please help me, my concern is that this laptop has some important documents that I think I could get back by removing the hard drive but my biggest concern is that there are a lot of bookmarks in my browser with a lot of passwords for services and stuff I don't use daily, but when I'll need them, I'll run into trouble, not all accounts where created with my main, current email so I can't really recover passwords.