I may be wrong here but from my eexperience, you might be stuck with a script that won't let you transfer calls to a higher level until the script is ready and the caller is annoyed.

If you have ever called a customer support line then you'll know exactly what I am talking about. I'd also find out what problem tracking software/script they use and get familiar with it. Also, try to make friends with the higher admins and try to hang around with them when not at work. Unfortunately, some admins still treat lower level people the same way that Nick Burns (Saturday Night Live, NBC), treated his users. Sometimes administrators tend to forget that at one tiime that they too were an end user.
Also, practice problem solving skills, if possible setup an extra computer at home just for this person and have an experiened admin mess the system up and then try to solve the problem. Also try to research and find the solution on your own and document your research if you do need to escalate the problem.
Always remember, you never get done learning, I just graduated from college and I just now found out that Windows also has symbolic links just like Linux (except for the \'s) so now I can do my program files directory like \usr\bin and my profile directory is \usr\home. (Symbolic links are directory names that simply point to the real directory)
Last but not least, practice good communication skills, spelling and grammar are important as well as speaking fluent and correct English (I don't mean to offend you if your actually in India but I have called support lines where the rep had a 12 syllable name that I could never pronounce and had a hard time understanding what he was trying to say).
I don't mean to discourage you but the company may have QA (Quality Assurance) and AHT (Average Handling Time) rules that need to be followed as well.
I'd also study for at least the A+ exam and try to get certified.
I hope this helps you,
Jeff
References:
Your Company's Computer Guy [Television sketch]. (1976). Saturday Night Live. National Broadcasting Company.
New York, NY.