SQL Server 2012 :: Trigger For Update Action Without Primary Key

I am writing a trigger for getting values to auditlog table when the values gets updated. Below is the code of my trigger.

CREATE TRIGGER [dbo].[Update_Temp] ON [dbo].[Temptable1] FOR UPDATE
AS
DECLARE @bit INT ,
@field INT ,
@maxfield INT ,
@char INT ,
@fieldname VARCHAR(128) ,
@TableName VARCHAR(128) ,

[Code] ....

The code is working fine when the table has primary key associated. However due to some restrictions I will not be able to have a primary key for some tables. I want to implement the same trigger in those tables too. When there is primary key, that primary key needs to get inserted into the audit table and if there is no primary key, i want a specific column value to get inserted instead of the primary key value into the audit table.

For example, i have a student table in which there is a student id, name, dob. there is no primary key defined for the table. So when i update the name or dob, i need the student id to get inserted into the Pk column of the audit table.

I tried modifying the code by checking the @pkcols for Null and if its null to get the old value as the primary key however I was not able to do it .