The relationship between news sentiment and financial market behavior has emerged as a critical area of study for investors, analysts, and policymakers. This comprehensive research paper integrates multiple analytical approaches to quantitatively analyze and forecast the impact of news on U.S. companies (both public and private) and broader markets across all sectors over the past decade (1990-2025). We leverage historical news data from the nation's top newspapers and financial outlets, applying advanced quantitative methods to measure correlations between news events and market movements. Our integrated framework combines econometric time-series models (VAR, ARIMAX), jump diffusion approaches, and machine learning techniques (transformer-based NLP and deep regression) to capture the direction, magnitude, and decay of news impacts. The analysis reveals that significant news events across political, economic, regulatory, earnings, M&A, product, legal, and geopolitical categories can trigger immediate stock price moves and volatility spikes, with effects that often persist for days. We document asymmetric market reactions where positive news tends to prompt rapid upward price adjustments, whereas negative news can have prolonged or delayed market reactions. Our research also demonstrates the importance of network effects, wherein news about one company can influence the stock prices of related firms through industry or macroeconomic linkages, creating sentiment contagion patterns across markets. Building on these insights, we propose a suite of real-time capable algorithms for news sentiment extraction, impact scoring, impact duration forecasting, and cross-news correlation modeling. Throughout, we ground our models in rigorous mathematical frameworks and draw inspiration from neural network structures and logical reasoning to conceptually guide model design. We include advanced visualizations to illustrate correlation networks, signal propagation through markets, and the performance of our forecasting approaches. The integrated real-time prediction system demonstrates improved accuracy in forecasting market responses as new headlines break, offering practical applications for investment strategies, risk management, and market surveillance.