Re: problem in grounding
I spotted 3 things, 2 of which are the possible cause.
Try connecting a 1k resistor from the counter reset input to ground, you have them just floating.
Also connect a 1 k from the first 4026 start/stop input to +v, again you have it just floating.
Floating inputs on these ic's will make them susceptable to noise on their inputs, grounding the whole circuit may well reduce this and make it work, at least for a while.
Also you have a 330r resistor and an unmarked device from the 555 pin 3 to ground, what purpose does this serve?, it'll probably work better without.