There are numerous safety interlocks on a boiler: low pressure switch, high overtemp switch, aquastat, flame sensor, (and maybe a flue pressure detector). There could be others. It sort of sounds like the system is not detecting the flame, and then does a safety shutdown. Often, it will sit for say 10-minutes or so to allow gas to dissipate, then try again. After a few tries, it gives up. There's often an indicator light that may be flashing a code. Course, you need to know where it is and what the code means.
Sounds like you don't have the knowledge or skills to fix this, so it's time for a pro. There should be a wiring diagram somewhere pasted inside of the cover. If you can decipher the symbols, you should be able to follow the interlocks to see where it is open. If you are lucky, it could just be you need to clean the flame detector. You might need some new parts...hard to say without being there. The low-voltage interlock signals are usually 24vac, so if you can follow that path, see where it stops and that's the switch or interlock that isn't working. Now, it could be a bad device, or it could just be open because the thing it is measuring is out of tolerance...you'd need to know what it is measuring, and test for that. Sometimes, you can take it out and say put it in a pan of water on the stove (on say an aquastat) and see when it opens or closes as you monitor things with a themometer and a meter. It's not rocket science, but it can get complicated, especially deciphering the symbology on the diagram.