Joomla- Mysql Webserver First Byte Time taking too long

Dear Experts,
Im new to this forum. Our University web server at www.sastra.edu uses Joomla 2.5-Mysql- IIS 7.5- Windows Server 2008 R2. The loading time of the home page is taking too long. Kindly help me pls. Thanks in advance for your time. Upgraded to Joomla 3.7 but problem is persistent.

No virus/ malware issue. The home page size is 750 kb.
I find a lot of sleeping threads in the Mysql user connections.
webpagetest results are given below

Details
First Byte Time (back-end processing): 0/100
24093 ms First Byte Time
ms Target First Byte Time

Use persistent connections (keep alive): 100/100

Use gzip compression for transferring compressable responses: 96/100
112.3 KB total in compressible text, target size = 108.7 KB - potential savings = 3.5 KB

FAILED - (2.5 KB, compressed = 0.6 KB - savings of 1.8 KB) - http://www.sastra.edu/modules/mod_vtem_news_stack/css/styles.css
FAILED - (2.6 KB, compressed = 0.9 KB - savings of 1.7 KB) - http://www.sastra.edu/modules/mod_globalnews/scripts/browser.js

Compress Images: 87/100
599.7 KB total in images, target size = 525.4 KB - potential savings = 74.3 KB

FAILED - (63.6 KB, compressed = 29.0 KB - savings of 34.7 KB) - http://www.sastra.edu/templates/santosh/images/nirf2.jpg
FAILED - (61.4 KB, compressed = 28.1 KB - savings of 33.4 KB) - http://www.sastra.edu/templates/santosh/images/nirf1.jpg
FAILED - (9.8 KB, compressed = 4.8 KB - savings of 4.9 KB) - http://www.sastra.edu/images/sastra/atsym.jpg
WARNING - (76.2 KB, compressed = 74.8 KB - savings of 1.4 KB) - http://www.sastra.edu/images/sastra/slider/THE_Ranking_1.jpg
Warm regards
Shankar sriram