Format cell color based on multiple cell values

I want the background color for cell A1 to be purple (13) if any of the below statements are true:

B42>"" and G42="" or
B43>"" and G43="" or
B44>"" and G44="" or
B45>"" and G45=""

Or you could look at it this way:

B42 NOT ISBLANK and G42 ISBLANK or
B43 NOT ISBLANK and G43 ISBLANK or
B44 NOT ISBLANK and G44 ISBLANK or
B45 NOT ISBLANK and G45 ISBLANK or

Conditional formatting will only allow three conditions. Is there code I can use in the worksheet event to get this to work?

B42, B43, B44, B45 are all fields called Hospital Admit Dates. G42, G43, G44, G45, are all Discharge Dates. A person can have several hospital admissions so I've made room for 4 admit dates and 4 corresponding discharge dates. If the person is in the hospital, I want cell A1 to be purple.

If any of the B cells contain a date and the corresponding G cell does not contain a date, the person is in the hospital because there's no discharge date in the corresponding G cell but there is a date in the admit B cell.

My brain is stuck in a vicious looping cycle so I can't think straight and don't know if this is possible.

I'm using Excel 2002 and am not great at fixing syntax errors. I've tried several things but when I use your code in the conditional formatting it tells me the formula contains an error. Do you know what I need to maybe add or remove?

=OR(AND(B42<>"",G42=""),AND(B43<>"",G43=""),AND(B44<>"",G44=""),AND(B45<>"",G45=""))

Sorry, my mistake. There was a space in the cell reference B44. Your code works perfect. Thanks so much!!