There are several things happening here which are less than ideal.
In the first place, you can't starve the kid into eating food she doesn't want to eat. What you can do is insist that she try at least one bite of a new food. If she doesn't, she gets 10 minutes in a timeout room (this should NOT be HER room like my parents did - all her stuff is in there, how is it punishment to be sent to HER room
) 10 minutes later, you go in and ask if she understands why she is in there. Make her explain to you why she's in there - - just to be sure that she really does understand it. Ask her if she would like to try the bite of food now so she can come out of the timeout room, or would she rather spend another 10 minutes in the room. She might just choose to stay there. If so, repeat yourself, but add 5 minutes to the time every other time you do it. Also, of course, make sure that even though it's not her room, there's nothing of entertainment value in there. The timeout room in my house is a 2nd guest bedroom that we NEVER use. It has a bed and 4 bare walls. The kid doesn't like it much in there.
Eventually she'll decide that eating one bite of food in order to gain her freedom sounds like a pretty good idea.
I also noticed that you seem to be allowing her to drink sodas. First off, just from a dietary standpoint, a 4 year old does NOT need sodas. Hell a 40 year old doesn't need the things, but a kid certainly shouldn't have it at that age.
Diet aside, if you keep giving the kid sugary stuff like sodas, candy, etc, then she's less likely to be willing to try non-junk foods for two reason. 1) kids want a daily sugar intake that's enough to crystalize an ant colony. They'd eat it straight out of the bag if you'd let them. Give 'em too much, and they start not wanting to eat anything unless it's loaded with sugar. 2) sugar fills 'em up FAST. So, for example, if your daughter had a coke at 3:30 and then you put food in front of her at 5, and it's not more sugar, she's not gonna feel hungry.
Bottom line? Kids must be taught that what the parent says, goes. I'm not saying you have to be a dictator, but they must understand that the house is not a democracy, and they do not have a voice in their fate unless you allow them to have one. If you tell the kid to eat one bite of food, the kid must understand that not eating it will result in immediate consequences.
On the flip side, if she does eat it, and honestly hates it, I wouldn't make her eat more of it as long as there were enough other foods that she liked that she could get a balanced diet.