After 5 years of working, SQL Server 2k5 Table now locking without any changes made to DB
Use SQL Profiler to trace your deadlocks and find a few example queries that are the root cause.

Then copy that SQL to SSMS and view the execution plan for it.

Look to see what kind of locks are being held when the query runs.

It's almost certain that you are experiencing table locks - actually, as you state, someone removed row-level locks and page-level locks. 

You have options:


Modify your SELECT statement to use READ UNCOMMITTED or (nolock). This means this query can read dirty data. Only you will know whether this will be acceptable with your data set - very often, it is fine to have dirty reads and doesn't impact the functionality of the system.
Use row-level locks. You can force these using a query hint.
Use row-versioning - this option means the updates operate on a different version of the rows to the ones that the SELECT statement is reading from avoiding deadlocks altogether.


You can find out more details about row versioning and other deadlock reducing techniques here.