The screws in the bottom plate normally would have no way of causing the computer not to power on. If the bottom plate is safely in position, the machine should be able to power on even with the screws fully removed. It would be a good idea for you to locate the serial number on your machine so you can determine the model. If the bottom plate is split, then you should be able to locate the serial number by removing the battery and looking for a sticker with the serial number printed on it in the battery bay. You can then enter your serial number at [link|https://checkcoverage.apple.com|checkcoverage.apple.com] to determine the model. Once you know the model you can try to find the screws for sale here on iFixit. My guess is [product|IF160-021|these] will include the screws you’re looking for.