I've done a bit of legwork for you by filling in a calculator with relevant values based on your question-->
http://bitcoinx.com/profit/index.php?hashrate=400&cost=350&electricity=0.15&power=220&months=3.0000&decline=0.50In that filled out calculator (see^), I've simplified and swung the numbers in your favor by quite a bit in terms of values and circumstance.
Look at the calculator I've filled in alongside while I explain why even with this handicapping of figures you'd be foolhearty to begin mining along the mindset of the approach you asked about:
I've assumed you spend that $350 on a new AMD 6970 placed in a current system- I'll reference this in the proceeding...
- The second box's value of 50BTC/block is a lofty, but unachievable (realistically)
- the 'hash rate' box I filled with a value attainable on a 6970 with a mild overclock
- in the next box I left the.15 cents/K=kWh but it depends on what you pay where you live (I have a rate of 13.5 cents/kWh)
- in filling in the pwr consumption box with 220W I've given you a huge break- this figure discounts the remaining non-gpu portion of your hypothetical computer. Also, 220W is a bit low considering the overclock to reach 400MH/s
- I left the timeframe at a quarter of a year
- $350 is ONLY the cost of a GPU NOT a new computer as you asked about
Since it wasn't directly answered above, I'll also tell you that you can find a conversion rate for BTC/$ at any of the exchanges, and a site like
http://www.bitcoincharts.com will show you an overview of the latest exchange prices.
Use the calculator provided above to see how many BTC/day you could mine, and you'll see that if things work out well (prices stay the same or go up, difficulty stays the same or lower) then you could be making $1.53/day before electricity costs!

Of course if you're like me, you can "justify" buying a new computer/new graphics card (6870 for $185) on the assumption that you needed a new graphics card, and hey, if you make any money back mining with it, good for you.
Good luck.