Force SQL Server to run query conditions as written?

You are falling into the "Catch-All Query" trap, which is explained very well by Gail Shaw here.

To summarize the problem: SQL Server optimizes away the significant overhead of query compilation by caching a query plan after compilation, and then later checking the cache for a matching query plan before a later compilation. The "matching" that occurs here is purely textual, so the actual value of a variable will not affect this.

That's good 99% of the time, but in some cases it's bad. One case where it's bad is when someone tries to construct a WHERE clause as though its like a short-circuiting IF statement in C, etc. This doesn't work well, because the SQL compiler has to make one query plan that will work regardless of what the parameter values actually are, and the only way that it can handle these "clever" logical switching-conditions in the WHERE clause is to make a simple brute-force plan that just scans the whole table, filtering the rows as it goes, without leveraging any indexes.

Not suprisingly, this makes them uniformly slow, no matter what the parameter/variable values are.

There is no guaranteed way to force SQL server to execute your clause conditions in a specific sequence. The optimizer will always evaluate them in the order it sees fit.

What you can do is something like this:

IF @LinkMode IS NULL
BEGIN
    select ...
    from ...
    WHERE (myColumn IN (...very long time exeted query...))
         ...
         ...
END
ELSE
BEGIN
    select ...
    from ...
    WHERE ...
         ...
END

If it is an option, use an IF statement to execute the appropriate form of the query. Also, in SQL, you tell the db engine what to do, not how to do it - things are not executed from beginning to end. It can be hard to predict what exactly it will do. You probably know this though ;)