I found the "lock" by removing the center drawer -- it's a smallish metal bar on the side of the stuck top drawer, towards the rear. But, on my desk it seems to be jammed and I haven't been able to shake it loose. I'm going to try WD-40. Ideally once the top drawer is opened, the lower one will too. Good luck.
Did you ever get your desk opened? I have the same problem with our old wood desk. The drawers on the right side don't open, but the ones on the left do, as does the center drawer. There is no actual lock on the desk, but the right drawers are "jammed" shut, probably some safety mechanism. How do I get it to release? My husband told me once how to do this, I think it's a combination of positions of some of the drawers, or something like that. Sadly, my husband died a month ago, and now I need to get into the desk. Any suggestions, anyone?