Yep, I say buy a new bike. Conversion builds can be tricky, too. I know I had to use a friend's tools to install my BB and headset.

Besides, like others said, you will be waiting for parts for a while. And you will go crazy thinking about which part to buy for every piece of the bike (which crank should I get? Which wheels? Which cog? etc) overall, if you have the cash, it's less stressful to just buy the bike and focus on riding it.