Building a PC isn't as hard, or as complicated as it looks. It can seem a very daunting task to anyone who has never attempted it, but it is really not that complicated.
And building a MAME cabinet is great fun. It does depend how far you want to go with such a project though. Do you just want an arcade style joystick setup, and a PC setup to run MAME and other emulators? Or are you thinking on a larger scale with a full sized arcade cabinet and controls, with a PC inside?