When a prefix is used "productively" (when a modern English speaker coins a word by combining a prefix with an English word, as in "preboard" meaning "board ahead of time", "reorder" meaning "order again", or "cofound" meaning "found with someone else") it generally doesn't change the pronunciation of the base. Most productive prefixes take some kind of stress (either secondary or primary) and the base keeps some kind of stress in its original position.
However, there are words that in a historical or etymological sense contain prefixes, but that aren't pronounced in modern English with the same pronunciation as the original base word. Sometimes these words were formed by prefixation in another language (like Greek, Latin or French), or sometimes the word was created by English speakers, but the pronunciation is based on analogy to the way that we pronounce words that were formed in those languages.
finite and infinite: etymologically, infinite starts with the negative prefix in-, from Latin, and has the same base as finite, but in English, they are pronounced differently due to the different stress patterns.
solve and resolve: etymologically, resolve starts with the prefix re-, and has the same base as solve, but in English, they are pronounced with different consonant sounds (/s/ and /z/).
John Wells's phonetic blog has a post on words starting with re-, de- and pre- that gives more examples of words that etymologically contain these "prefixes", but have different stress patterns than words that were formed in English by productive use of the prefixes pronounced [ri], [di] and [pri].