Unfortunately the name El Dorado/Eldorado was one of the most used names for gold mines and gold mining operations. You will need to say where the deed, or claim, or whatever it is you have on your certificate is from. If you have an exact name or region of the town it would help. Names on the certificate would help. You already gave a date and that might be good info.
There was an operation called the Eldorado Gulch Gold Mine that was in the Washington Gulch in Montana. It was also called the Jefferson Gulch and Buffalo Gulch. The mine was in operation from 1933 to 1937. Like most placer claims, once the gold is gone the mine is closed. There's no reason to keep digging once all of the loose gravel and overburden has been processed. That's what placer mining is. They just work the gravel that has gold in it that has somehow moved from the origin of the gold in hard rock. It can move by water, normal erosion, rockslide, etc. Taking gold from the hard rock is called Lode mining.
Now back to the mine. The Eldorado was a strong operation that used state of the art equipment for it's time. It worked 1,000 cubic yards of gravel per day and that is likely why they were only in operation for 4 years. Once they had worked and washed all of the avalable soil there was nothing lse they could do. When your mom said they had lost everything it is probably because they made less money than they had spent to buy those state of the art machines. Keep in mind that they were in the midst of a depression too. The very fact that they started a mining operation in 1933, when things were at their worst is an indication that somebody was hoping against hope that they were going to hit the motherlode. I'm surprised that your grandparents even had money to invest in 1933, and I don't mean to hurt any feelings, but it might be that they too were hoping against hope.
Anyway, with names, region or town name, and any other information you could give I might be able to get more info for you. Since you said the certificate stated it was non-transferable it is basically worth noting. Had this mine been a giant in the world of mining then it might be worth something to history buffs, but this Eldorado went bust in 4 years, so that's not the case. Sorry.
