If it sounds like it is booting normally (you can hear the startup sound/hdd access), but there is no display the monitor may have died. The VGA/Hires mod runs the internal monitor at a higher voltage and scan frequency than it was designed for, some of these old monitors just can't take the abuse for too long.
If you can't hear it booting than you may be lucky. The problem may not be the internal monitor. Some Mac LCs (the Color Classic is based on the LC2) will act completely dead if the PRAM is corrupted. Replace the PRAM battery, hit the CUDA switch on the motherboard, command+option+P+R on boot.
For a longer life stick to the original 512x384 mode. Most stuff that will run on a stock color classic (LC2) will run in that mode. I really don't see the point in running the monitor at 640x480 unless you also upgrade the CPU.
The best way to upgrade the internal monitor would be to use the board from the Amstrad monitor that used the same CRT. It will do up to 800x600 quite happily (believe it or not it is readable). That would be a LOT of work and the donor Amstad monitors are also pretty hard to find now.