Welcome fellow SE/30 owner.
In my experience, pressing the Reset button on the left side of the Mac will often bypass the RAM startup checks. I have 128MB of RAM on my SE/30, and it takes well over a minute to check all that RAM, during which time my screen displays these strange artifacts. But once the RAM checking concludes, the machine boots normally. So you should try waiting longer, like 2-3 minutes and see if the machine finally boots. If it does, you have nothing to worry about.
Now despite what I have written about RAM checks, it still very well could be you need to change the capacitors. If no one has done a cap job on your logic board before, I would say with 90% certainty that you do need to change the caps, as do most SE/30 motherboards by now. This topic has been discussed endlessly on this site before, so a quick search should yield the info. Here is a cap job thread, for example.
In my experience, pressing the Reset button on the left side of the Mac will often bypass the RAM startup checks. I have 128MB of RAM on my SE/30, and it takes well over a minute to check all that RAM, during which time my screen displays these strange artifacts. But once the RAM checking concludes, the machine boots normally. So you should try waiting longer, like 2-3 minutes and see if the machine finally boots. If it does, you have nothing to worry about.
Now despite what I have written about RAM checks, it still very well could be you need to change the capacitors. If no one has done a cap job on your logic board before, I would say with 90% certainty that you do need to change the caps, as do most SE/30 motherboards by now. This topic has been discussed endlessly on this site before, so a quick search should yield the info. Here is a cap job thread, for example.