Laptop Powers on for just a second then turns off

I picked up an old dell 14 5842 (or maybe 5841?) from a friend who couldn't get it to work. Ive got a spare 45W dell brand AC adapter plugged in, and when i hit the power button the charging loght turns on, but nothing else happens, no fan or anything, then it turns off.

I plugged in a usb powered phone cooling fan and hit the power button again, and that goes on for about a half a second before losing power. I've tried power cycling, changing the RAM, and unplugging the battery and using just the AC adapter. No results with anything.

I don't have immediate access to a multimeter, but I suspect something may be short circuited. I also dont have access to a replacement battery, and I both doubt that is the issue and am hesitant to buy one if it wont help.

Any suggestions on what else I might try or ideas as to what the issue might be?