What year would it be 1 billion minutes ago?

1,000,000,000 minutes ago would be around the year 108.

How to work it out:

1,000,000,000 minutes / 60 = 16,666,667 hours

16,666,667 hours / 24 = 694,444 days

694,444 days / 365 = 1,902 years

2010 - 1901 = 108

* note this is a rough working out, not exact figures, all numbers have been rounded, and leap years haven't been taken account.