Electrical issues in home?

Have you got a tumble dryer plugged into a gang socket with something else.  This will force your electricity to keep tripping.

If you replaced the main box and all the breakers, but failed to replace wiring throughout the house, you've failed to improve your electric situation. The power box is usually the culprit--but to hook up a new box to old, bad wiring won't help much. Have an electrician come and evaluate the situation before your house burns down from a short or arc. 

Do you have a question?

Clearly the circuit breakers weren't your only problem. This is a case where you should get a competent electrician in to check your entire wiring and system.  You may have issues elsewhere, especially if this an old house.  I suggest you get this done sooner rather than later.

It may turn out to be a problem with your outside supply but you definitely need the house to be checked first.

no breakers tripped? look at the point of attachment where the supply enters the building or lose wires on the main switch or neutral. if a breaker tripped whats plugged into it compared to its rating or just tong it and see how much current is passing thru it.

Better to be safe than sorry.  Advisable to get a couple of quotes and compare, if I were you I won't waste time.

If you had the breakers replaced by a COMPETENT electrician, there is NO WAY anything remotely like what you describe would occur. Even if 100% of the wiring after the breaker was the actual cause, the electrician would have inspected that before replacing the breakers. It can't be the panel itself, because a competent person would replace that with the breakers.

Therefore, exactly 2 possibilities remain.

1. You are FLAT OUT LYING.

2. You had the work done by someone that is COMPLETELY INCOMPETENT.

possibles: the breaker box itself is so old that it no longer holds the breakers securely. next possible: one of the circuits has an intermittent open ... it opens and closes and you don't know ... it, therefore adds and removes a fairly large load [light load wouldn't do it]. Something like a water heater. you test this by turning off each of the large circuits in turn and trying to reproduce the problem. next possible: something [probably large] creates back EMF when starting up ... this would be a motor of some kind, probably at least one horsepower. next possible: somewhere hidden, your system has been tapped to power a room or rooms that you don't know about ... and this happens when their load is added to your load ... almost reaching the limit of what you main breaker can handle [like a hidden grow room for weed].

There might be to many appliances dragging off any given circuit causing a trip to function - However, if it's not rated correctly, which it won't be with old wires and new breakers there will be less resistivity causing dimming of lights etc.

This is due to excessive heat.

Other than that, it could the local grid.

I lived in a place like that where our neighbourhood circuit was a bit dodgy.

I suggest you get an electrican out before someone gets killed.