Hi Niki, welcome to the board.
This is going to take a bit of explaining and that explanation makes a few assumptions that, hopefully you can re-arrange and make work for you.
First, the assumptions.
You have a data range of 5 columns, say columns G to K.
These columns are:
Customer name, Lawn size, Total price, Amount paid and Amount owed.
(Say a range of G2:K11 with G1:K1 being the column headers listed above.)
Now, say you want the 'dropdown' to be in cell A1.
For this exorcise we'll use Data Validation in A1.
Make your validation a List and make it refer to the range G2:G11.
(Now when you click the dropdown arrow in A1 you should see your list of names from G2:G11)
Now, in cells B1 through E1 we can use some VLOOKUP formulas.
In B1, enter the following: =IF(A1="","",VLOOKUP(A1,G2:K11,2,0))
In C1, enter the following: =IF(A1="","",VLOOKUP(A1,G2:K11,3,0))
In D1, enter the following: =IF(A1="","",VLOOKUP(A1,G2:K11,4,0))
In E1, enter the following: =IF(A1="","",VLOOKUP(A1,G2:K11,5,0))
This will show the lawn size, total price, the amount paid and the amount still owed for the name selected from the dropdown in A1.
Next, simply use Conditional Formatting in cell E1 with the rule being: if the value is greater than 0, format to red (or whatever).
Unfortunately, I can't really tell you where to find all the things mentioned to do this as I don't know what version of excel you're using. (I'm only using 2003 here and my 07 is at home, so if you're on anything newer than 03 I can't walk you through any of that.)
Hope (at least some of) this helps.
I see Howard was posting while I was still typing, so you might already be set...