The BIOS won't post if it doesn't like the memory. It's possible the flashing is a replacement for beeping, not sure your laptop has a speaker on the motherboard.
Not all PC133 memory is the same. It is possible you are experiencing a compatibility issue with your Dell with voltage, timings, or density. Here is what Crucial recommends for your laptop:
http://www.crucial.com/upgrade/compatible-memory-for/Dell/Latitude%20C600%20Series/list.html
According to that link, the memory specs you needs are
SDRAM, PC133 • CL=2 (timings) • Non-parity • 133MHz • 3.3V (voltage) • 32Meg x 64 (this is the memory density)•
Make sure the memory you purchased matches these settings. It's possible the memory you have is more dense and is unsupported. It's also possible that your memory is less dense, but is double-sided (which also tends to be unsupported on some computers). The timings might also be off, and I doubt your BIOS is able to recognize anything other than the factory-specified default. Also make sure the memory you are inserting is not buffered or ECC memory, your laptop will not support this.
If you can return that memory, it might be better to buy memory that is specifically stated to support your laptop (i.e. google "dell inspiron C600 memory upgrade"). I found memory guaranteed to be compatible for $30/dimm if its worth it to you.
I'm also not too sure Crucial is 100% correct when they say PC133 will work. I've heard of computers not being too happy with PC133 even though it should be capable of reverting to PC100 (though, again, that might be timings and density and not necessarily the speed).