Air Conditioning - a/c problems in new home

I Just Moved Into A New Home And When We Had The Inspection The A/c Turned On And Cooled Very Fast. It Is Starting To Get Hot In St. Louis And My A/c Is Not Cooling The Top 2 Floors Of My House. I Have Changed My Filter And I Think I Am Setting My Honeywell Thermostat Correctly, But Still No Cool Air Out Of The Open Vents. The Down Stairs Is Cool, But Nowhere Else. I Turned It Off After Running It For A Couple Of Days And There Is Water Coming From The Furnace/ A/c Unit In The Basement. The Water Is All Around To The Drain In The Floor. What Is Wrong? Is There Something I Can Do Or Do I Need To Call A Heating And Cooling Guy?
Since I Just Moved In I Am Trying To Spend As Little More Money As Possible, But I Really Want My A/c To Work Correctly. Anyone Have Any Ideas? Thanks, Joe

A couple of things..

Since you said you are not getting air flow up stairs, i'd check to see if the coil is clean.. It will be hard to get to.. but let's look at other things..

For water, I'd check to make sure the drain is clear. Are you getting frost on the line??

Blower cage clean? Sounds like you got the fitler taken cared of..

Any air flow in the vent up stairs?? Return??

I've Checked Everything I Can See Without Taking The Unit Apart. Everything Looks Clean. THE LINES ARE GETTING DAMP AND KIND OF FROSTY WHEN I LET IT RUN. The Blower Is Working, But I Still Don't Feel Any Air From The Vents On The 2 Upper Floors. I'll Check The Unit Further When I Get Home From Work. Thanks For Your Reply!

THE LINES ARE GETTING DAMP AND KIND OF FROSTY WHEN I LET IT RUN. The Blower Is Working, But I Still Don't Feel Any Air From The Vents On The 2 Upper Floors.

You say new home???? How old is the unit then????
Sounds like your low on freon and the coil is iceing up. Id call a tech Make sure he goes over the unit for any leaks. See if you can find out the last time anyone put freon in it. this will help the tech

ED ;)

Thanks For The Advice, I Cleaned Out Everything And It Is Working Fine.