The 28c64 is a byte-wide EEPROM; it's not a microcontroller and won't do anything except store data. As you've noticed, it has a lot more pins than an arduino can easily control.
The PIC16F629 is a small, 8-pin PIC microcontroller with a whopping 1k words of flash memory (approximately equivalent to 2k bytes on an AVR) and 64 bytes of RAM (very small.) It is not compatible with the AVRs used in Arduino, and you would need to buy a C compiler for it (or download a "demo" version.) It would not be programmable from the Arduino environment, and it also requires a switched 12V "Vpp" supply for programming, so it wouldn't be trivial to use an Arduino for programming it, even given compilers to generate the code to be programmed.
Your best bet at your current level of expertise probably involves finding someone who would be interested in trading your chips for some AVRs... The 629s are roughly equivalent to an ATtiny13, worth about $1 each. The 28c64 is pretty obsolete.