Heart disease can be life-threatening if not detected and treated at an early stage. The electrocardiogram (ECG) plays a vital role in classifying cardiovascular diseases, and often physicians and medical researchers examine paper-based ECG images for cardiac diagnosis. An automated heart disease prediction system might help to classify heart diseases accurately at an early stage. This study aims to classify cardiac diseases into five classes with paper-based ECG images using a deep learning approach with the highest possible accuracy and the lowest possible time complexity. This research consists of two approaches. In the first approach, five deep learning models, InceptionV3, ResNet50, MobileNetV2, VGG19, and DenseNet201, are employed. In the second approach, an integrated deep learning model (InRes-106) is introduced, combining InceptionV3 and ResNet50. This model is developed as a deep convolutional neural network capable of extracting hidden and high-level features from images. An ablation study is conducted on the proposed model altering several components and hyperparameters, improving the performance even further. Before training the model, several image pre-processing techniques are employed to remove artifacts and enhance the image quality. Our proposed hybrid InRes-106 model performed best with a testing accuracy of 98.34%. The InceptionV3 model acquired a testing accuracy of 90.56%, the ResNet50 89.63%, the DenseNet201 88.94%, the VGG19 87.87%, and the MobileNetV2 achieved 80.56% testing accuracy. The model is trained with a k-fold cross-validation technique with different k values to evaluate the robustness further. Although the dataset contains a limited number of complex ECG images, our proposed approach, based on various image pre-processing techniques, model fine-tuning, and ablation studies, can effectively diagnose cardiac diseases.