Multiple =If(and(.....)) function in one cell

Hi,
I am trying to create an automated spreadsheet that will look at several conditions in one cell based on a drop down menu in a different row that is comparing information in a different sheet.
I was able to do this type of an equation only using the IF function, for a simpler automation in the same sheet.
So here is what I am trying to accomplish in more detail:

The function looks at the calculated elapsed years in a different cell. It takes that information and determines whether or not the time is less than or more than a certain amount, then it also has to look at what is displayed in the specific cell that is referenced in sheet 1 (named "database")(same excel book.) Based on that information it gives me a reading weather the issue is "Time barred" or "To be determined."
My problem comes up when I try to enter multiple equations like it in one cell, where it has to calculate a different elapsed years and look at a different cell in sheet 1 to determine what it says.
My equation so far is: =IF(AND(H3>=1,AND(A5=Database!$A$5)),("Issue is time barred"),("Analysis to be Determined")) If I have this alone it works, but when I try to add more formulas to the same cell and change out where H3>=n and A5=Database$x$n; then the equation stops working.

Basic breakdown of the formula that works:

H3 is cell where calculation for elapsed years occurs (that cell alone has a basic calculation)
1 refers to allowed years for warranty (the number changes based on the warranty for that object)
A5 is the cell where the drop down menu occurs and phrasing (wording) is selected based on the information in sheet one-labeled database
Database-is the main category that is used for reference only (does not contain any formulas) for the master sheet (where all the equations take place and the area of my concern)
$A$5 is the cell number that contains the text that is referenced in the sheet 1 or "database"

If anyone can help me out how to input more than one of these equations into a single cell that would be very much appreciated.
(I need 60 of these type of calculations per cell-that's my dilemma)

Thank you in advance for your time and for your help.