There's always some so-called language experts who will say some things
are not proper while others say there's nothing wrong with them.
However, you see "however" starting sentences all the time in reputable
publications.

Some examples in recent news stories:

"78%, expressed confidence in their companies' long-term success.
However, almost 50% said they were willing to turn to new jobs that
offered comparable packages."  Bangkok Post

"I will try to present an 'overview' of the entire subject. However, as
far as you are concerned, my answers to your queries are as follows:"
Jamaica Gleaner

"However, critics have questioned whether this target is achievable"
Scotland on Sunday

"TheCalifornian.com is pleased to be able to offer its users the
opportunity to make comments and hold conversations online. However, the
interactive nature of the Internet makes it impracticable for our staff
to monitor each and every posting."  The Salinas Californian

"The JVC KD-PDR30 looks and sounds good, and its standard iPod
connectivity will endear it to those looking to take their iTunes on the
road. However, its lack of a decent search mechanism for navigating
large iPod lists means that it fails one of its primary usability
functions."  CBS News

"This month's Heroes Run benefit event has been postponed until next
year. However, plans are under way for two other events"  The Star