I have a generator rated 3000w/3500w surge was told that it would run my gas boiler OR TV fridge but not all. Is that right?
It should be able to feed all these appliances comfortably. Not one of these devices needs even 500 watts each. The fridge and boiler will each have a pump motor but not a very powerful one. If in doubt have a look at the information plate on each appliance and add all the wattages together. I'm betting they total less than 1000. But you need a safety device so that the mains and the generator can never be connected together, or else there will be an almighty bang. This will be a legal requirement and you'd be well advised to get a professional to wire it all up.
When you say 'rated at', do you mean the maximum output they quoted in the advertising or the real, sustainable output which will be less than that? Either way, it should easily provide enough power for a fridge, TV, lighting and gas boiler system at the same time. They are all low power devices. If it can't, then something is not right. If you start trying to use hair driers or electric heaters, it would get closer to its maximum output but, according to the rating, you have up to about 3 kW to play with. It should not care HOW you use it. The more current you draw, the harder the generator has to work so the more fuel it uses so you may need to fill its fuel tank more often if you use a lot of things at once.
A gas boiler typically only needs electricity for controls and for hydronic circulators. You would generally not select a generator that is undersized for the load, i.e., better to have slightly too much generator than even a little bit not enough. A fridge has a compressor motor that may require spikes of power each time cycles on, drawing three or four times its normal operating power. This dips into the surge specification on the generator. If you're anywhere near full capacity when that happens, you could fry the generator (or at least blow its breaker). You can look at the power ratings on your boiler, circulators, refrigerator and add in the lighting loads, to see whether you're more than half the capacity of the selected generator. Rule of thumb: combined refrigerator and warm air blower would be anywhere from 800 watts to 1400 watts. If they start at the same time, you would estimate the simultaneous, worst-case, max as, say, 5,200 watts of surge and plan accordingly. Or you could buy a measuring device ('Kill-A-Watt is a popular brand) and record the peak usage of each appliance and add those together. If you can guarantee that all appliances will start at different times, then you can reduce the maximum requirement. For example, when power goes out, you can plug in the fridge periodically, when you know everything else is either unplugged or has stabilized. The overload problem often occurs with a transfer switch that simply restarts everything at the same time. You can manually shed loads by switching off some of the devices when you transfer the load to the generator, then add them individually by switching them back on.
Yes the small unit you have will operate the gas boiler but I doubt it will run anything else. To run the fridge you need at least 8 amps steady draw for most units. and that is about 30% of the generator and when anything else is used the generator will lug down and soon be producing a lower voltage which will then burn out the appliance.
Don't know the drain of your appliances, particularly the boiler. 3000 watts is quite a lot, the tv and fridge don't use nearly that much, but the boiler is the unknown. Actually, it's not the boiler at all, but the fans and other electrics that make it work. There should be a tag on it somewhere that tells you what it's max draw is. Of course, the more you draw, the harder the generator has to work, and the more fuel you burn.