ur rig details are very low here.
but acording to your requirements... i will try to generalise this whole thing to give u an idea abt how much power is being used n how much will be used in order to increase that pc backup time from 1:45hr to 3hr....
We will Assume..
t = 1:45hr = 1.75hr
T = 3hr = 3hr
X = PC power Consumption Excluding the monitor/display
Y = Capacity of Your Inverter...
CRT Power Consumption = M = 90W (Maximum)
LCD Power Consumption = L = 35W (Minimum)
We have two equations as per ur provided info..
we have the following relation...
Inverter Capacity / (PC Power Consumption + Display Power Consumption) = Backup Time
i.e.
Y/(X + Monitor/Display Power) = Time
Y/(X + 90) = 1.75 -- eqnI
Y/(X + 35) = 3 --eqnII
solve both n u will get
Y = inverter capacity = 231W
X = PC power Consumption Excluding the monitor/display = 42W
X is very Low... even after considering the Worst CRT n the Best LCD
so CRT to LCD transition will not increase the backup time to 3hr.
...now some realtime calculation...
assuming X = 200W for ur rin...
Y/(200+90) = 1.75hr --> Y = 507W = ~500W inverter
gives
500/(200+35) = 2.12Hr --> around 2hr 7mins of backup..
that is 22mins extra after paying 12+ k for 22" LCD....
Better option is get a long lasting battery for ur inverter.