Mac Pro Tower 2009 powering up inconsistently

So here's a weird one. Similar to other's problems but with one strange difference.

Mac Pro Tower does one of three things

1) clicks on, no light, stuck

2) ckicks on, light, clicks off, no light,

3) powers up (good)

But the weird way I solve the boot problem is to remove the power cable, plug it back in, and hold the optical tray in place with my finger (opening up the silver door and pressing directly on the component tray) and it boots every time. I tried disconnecting the optical drive but it wouldn't boot at all in that configuration. I know there's several potential solutions here: power button battery, power supply, bad RAM. But would anyone venture a guess as to why holding the tray in place would allow it to boot every time?

I've confirmed there is nothing in the optical tray. There are no other startup disks. It does seem to check the optical drive during a successful boot though.

This is a refurb mac so I'm guessing that's why the the mac date is 2009 even though the MoBo is for a mid 2010. Not sure.

Mac Pro (Early 2009), 10.13.6

12 core Xeon 2.66 GHz

MacPro 5,1

16 GB RAM

Radeon HD 5870 graphics