You can use XQuery for this, but realize you are recreating key-value-pairs in XML, which negates the ability to use schemas or XQuery/XPATH in any reasonable manner. Consider changing the format to:
<root>
<APP_REG_NUMBER>AL/T/2010/86</APP_REG_NUMBER>
<SUBLINEID>235931</SUBLINEID>
</root>
I digress... the query you want is:
DECLARE @testXml xml = N'<root>
<Parameter><Param>APP_REG_NUMBER</Param><Value>AL/T/2010/86</Value></Parameter>
<Parameter><Param>SUBLINEID</Param><Value>235931</Value></Parameter>
</root>'
SELECT
@testXml.value('(//Parameter[Param/text()="APP_REG_NUMBER"]/Value)[1]', 'nvarchar(50)') as APP_REG_NUMBER,
@testXml.value('(//Parameter[Param/text()="SUBLINEID"]/Value)[1]', 'nvarchar(50)') as SUBLINEID
You use the //Parameter syntax to find all Parameter elements and then filter them ([Param/text()="foobar"]) to only those which have a child named Value that have the inner text of SUBLINEID. From there, you navigate to the /Value child element and return the first result ((query)[1]).