This prospective study investigated the association between elevated neutrophil-to-monocyte ratio (NMR), lymphocyte-to-monocyte ratio (LMR), C-reactive protein (CRP), procalcitonin, and tumor necrosis factor-alpha (TNF-alpha) and the risk of developing neurological complications in mechanically ventilated neonates. The aim was to evaluate these biomarkers’ predictive value for neurological complications. Within a one-year period from January to December 2022, this research encompassed neonates born at ≥35 weeks of gestational age who required mechanical ventilation in the neonatal intensive care unit (NICU) from the first day of life. Biomarkers were measured within the first 24 h and at 72 h. Sensitivity, specificity, and area under the curve (AUC) values were calculated for each biomarker to establish the best cutoff values for predicting neurological complications. The final analysis included a total of 85 newborns, of which 26 developed neurological complications and 59 without such complications. Among the studied biomarkers, TNF-alpha at >12.8 pg/mL in the first 24 h demonstrated the highest predictive value for neurological complications, with a sensitivity of 82%, specificity of 69%, and the highest AUC (0.574, p = 0.005). At 72 h, TNF-alpha levels greater than 14.3 pg/mL showed further increased predictive accuracy (sensitivity of 87%, specificity of 72%, AUC of 0.593, p < 0.001). The NMR also emerged as a significant predictor, with a cutoff value of >5.3 yielding a sensitivity of 78% and specificity of 67% (AUC of 0.562, p = 0.029) at 24 h, and a cutoff of >6.1 showing a sensitivity of 76% and specificity of 68% (AUC of 0.567, p = 0.025) at 72 h. Conversely, CRP and procalcitonin showed limited predictive value at both time points. This study identifies TNF-alpha and NMR as robust early predictors of neurological complications in mechanically ventilated neonates, underscoring their potential utility in guiding early intervention strategies. These findings highlight the importance of incorporating specific biomarker monitoring in the clinical management of at-risk neonates to mitigate the incidence of neurological complications.