Thank You Kappy
I deeply appreciate your quick response. Most of the steps I had already tried with no success. whatever was left out, after receiving your reply, I diligently tried and unfortunately all the measures failed except the last one which is to downgrade back to OS X.(I dont find any dmg file so easily. on appstore purchases , I do not see it either...)
Interestingly in the process, I had found out couple things which you may like to kindly comment on...
1) when kept, option key pressed while the system restarts(as control R won't work in my case), It shows up my SSID option and it does accept the password.
2) On digging further after I found out that there is nothing wrong with my hardware, I came across the following information.
(this is a cut -paste from the website where i had taken help to patch up High Sierra to install on my late 2009 mac mini)
.....
Known issues:
- Unsupported WiFi modules in some systems. Macs that use the Broadcom BCM4321 WiFi module will not have functional WiFi when running High Sierra. A fix for this is to open up your machine and install a compatible WiFi card. Machines affected include some MacPro3,1, MacBook5,2, MacBookPro4,1, iMac8,1, Macmini3,1, and MacBookAir2,1 systems. Please note that not all these machines will have an unsupported card, this is just a list of machines known to have shipped with that card in some configurations.
-- You can find out whether or not you have an unsupported card by opening System Profiler (About this Mac>System Report...), and clicking on WiFi under the Network section. Take note of the value listed for "Card Type".
IDs that DO NOT work under High Sierra:
- (0x14E4, 0x8C)
- (0x14E4, 0x9D)
- (0x14E4, 0x87)
- (0x14E4, 0x88)
- (0x14E4, 0x8B)
- (0x14E4, 0x89)
- (0x14E4, 0x90)
Any ID not listed, such as (0x14E4, 0x8D), is a supported card, and will work perfectly fine under High Sierra
So, I generated my System Report.
here is the screen shot.

I do not see any information about the card.
Is there any way to find it out?
Do you think if this is the issue then, downgrading back to OS X (capitan or whatever) should help?
Thanks in advance