anyone can suggest what program / approach I should use? I need to have a map like google map where I can display map, add marker polygon etc. But I cannot rely on such online services as client is afraid that such service die off and there goes our system...
Have a look at lots of resources pointed in answers to these questions on GIS.SE:
GIS for the web
Steps to Start Web Mapping
You might want to look at Google Fusion Tables, or solutions like MapBox or CartoDB for quick, hosted solutions.
Willing to invest more time (and depending on your skills and language preferences) you could delve into PostGIS & GeoServer / Mapserver with a frontend of OpenLayers / Leaflet (or any other libraries). OSGeo-Live DVD might come handy for a quick and dirty review of most of these options.
Here are pure open source based web map and geo-location database resources. Google map or Bing map is wonderful, but they require business contract for commercial use. It is said that Foursquare recently switched their map tool from Google map to open source based Leaflet API which looks like the picture below. This map tools is quite great and recommendable.

Good place to start. Two resources below are not really used for developers, cause those are already included in leaflet javascript API.
Map style : http://cloudmade.com/
Map data : http://www.openstreetmap.org/
Geo location based on ip address : http://dev.maxmind.com/geoip/geolite
Can download free ip address & city mapping file, which can be used for custom mapping code.
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