hi xyon,
welcome to ao and unfortunatelly some bad start

well i had very similar problem and if you look and search under some old posting with the ram you will be able to see it and find something usful there.

firstly putting new ram modules without knowing your motherboard is not good start at all.
You should know type of motherboard you have and then look on the site to peek into specification for it and see if ram you try to upgrade is suitable for your motheboard.
you dont want to get excited about having heaps of ram to find out its not appropriate for you mobo.

I dont know if you are familiar with hardware or you are newbie in that field too.
when you post in a future please put as many details you know about your pc so it will be easier to help you.
(type of motherboard,operating system, memory,cpu etc.)
also with bios type and sound you get from booting or not booting we can indentifie the poblem or at least go to right direction.
i did same thing like you and put 2 512 sticks in it and had burning smell and no booting but monitor didnt pass memory self test which indicate that it was problem with memory.
i went to shop and tried to by same mobo otherwise all my data would be lost(corect me guys if i am wrong here) and luckyly they didnt have it.i bought can of pressurised air and clean my slots nicely and next thing i booted with no problems except i didnt dare to put burned stick in it.
as suggested try empty slot first. can of air cost 5-6 dollars and you want be worse off you can clean your case too.
its not clear what is not working with your monitor?is it completely blank or what?
gl and keep posting but please before you spend any money get familiar with capabilities of your comonents and compatibility too. if not sure ask somone who is or post here for help.
gl