The aim of this work is computationally to correlate the synchronized neuronal activity of basal ganglia and slowing in theta and alpha rhythms in electroencephalogram (EEG) signal in thalamic region in case of dopamine depletion and decrease of synaptic connections. The used network topology is a scale-free network with constant node degree. The dopamine-modulated type Izikhevich neuron model is used for modeling the striatal region, consisting of fast-spiking interneurons, D1 and D2 type dopamine expressing medium spiny neurons. On the other hand, the ordinary Izikhevich neuron model is used in the modeling of extrastriatal basal ganglia (BG) regions where globus pallidus (GP) subregion neurons have also dopamine-dependent parameters. The thalamic region of the network is mass modeled including inhibitory input from basal ganglia. Depending on the decrease of synaptic connections and dopamine level, the synchronization among basal ganglia neuron populations is investigated. The effect of synaptic delay on synchronization is also considered. It is observed that the decrease of dopamine neurotransmitter and decrease in the number of synaptic connections cause an increased synchronous activity in BG. Also, slowing in theta and alpha bands in thalamus EEG signals is observed. This shows the causal relation between synchronization and power shifting to lower frequency components in the case of neurodegenerative diseases such as Parkinson's disease (PD).