Dealing with subjects who are unable to attain a proper level of performance, that is, those with brain-computer interface (BCI) illiteracy or BCI inefficients, is still a major issue in human electroencephalography (EEG) BCI systems. The most suitable approach to address this issue is to analyze the EEG signals of individual subjects independently recorded before the main BCI tasks, to evaluate their performance on these tasks. This study mainly focused on non-linear analyses and deep learning techniques to investigate the significant relationship between the intrinsic characteristics of a prior idle resting state and the subsequent BCI performance. To achieve this main objective, a public EEG motor/movement imagery dataset that constituted two individual EEG signals recorded from an idle resting state and a motor imagery BCI task was used in this study. For the EEG processing in the prior resting state, spectral analysis but also non-linear analyses, such as sample entropy, permutation entropy, and recurrent quantification analyses (RQA), were performed to obtain individual groups of EEG features to represent intrinsic EEG characteristics in the subject. For the EEG signals in the BCI tasks, four individual decoding methods, as a filter-bank common spatial pattern-based classifier and three types of convolution neural network-based classifiers, quantified the subsequent BCI performance in the subject. Statistical linear regression and ANOVA with analyses verified the significant relationship between non-linear EEG features in the prior resting state and three types of BCI performance as low-, intermediate-, and high-performance groups that were statistically discriminated by the subsequent BCI performance. As a result, we found that the frontal theta rhythm ranging from 4 to 8 Hz during the eyes open condition was highly associated with the subsequent BCI performance. The RQA findings that higher determinism and lower mean recurrent time were mainly observed in higher-performance groups indicate that more regular and stable properties in the EEG signals over the frontal regions during the prior resting state would provide a critical clue to assess an individual BCI ability in the following motor imagery task.