Why would there be no hydrocarbons in the Sveconorwegian belt?
There's a little more to it than its substantial age, but not a lot. 

First, a bit of background. We need a few conditions for accumulations of oil or gas:


A kerogen-rich source rock that has been 'cooked' to thermal maturity. Insufficient temperature, or insufficient time, and it's undercooked; if the temperature is too high, or the rock is very old, then the volatiles have all been discharged or cracked. I don't know of any source rocks older than about Ordovician; the best ones are Jurassic in age. 
A migration pathway from the source to a trapping configuration, and time for this to have happened.
A structural or stratigraphic trap, such as an anticline, and the geological conditions that have preserved it since filling. 
A reservoir rock — a porous and permeable rock. Usually this is a sedimentary rock, though hydrocarbons have been discovered in fractured granites (in Vietnam for example; this is rare).


Only 'conventional' hydrocarbon deposits need all these conditions (sometimes called a 'petroleum system', such as you might find in the North Sea). 'Shale gas' is basically just a mature source rock — we can extract hydrocarbons from it by fracking, for example. 

As you might guess from the list of conditions, there are lots of things that can destroy a hydrocarbon accumulation, or preclude its formation. For example, deep burial destroys porosity by diagenesis and compaction. Time increases the likelihood of trap leakage or thermal destruction of volatiles.

So, why no hydrocarbons in the (mostly Precambrian) Swedish-Norwegian shield? Maybe these are the top 3 reasons:


These old rocks never had a good source rock: too old, too little life. A bad start.
They are so old that any source would have been mature hundreds of millions of years ago.
In any case, metamorphosis has destroyed any potential reservoirs, and a combination of tectonism, orogenesis, and exhumation has destroyed any traps.