What "old internet companies" are you referring to? You gonna compare Google/Facebook to Altavista, Geocities or NetZero?
AOL? do i need to discuss this one?
Yahoo? read above.
Kodak? bankrupt.
SAP? Trying to sustain itself through buying other companies.
Motorola? good thing google is buying mobility. They completely failed. Android saved them from total disaster.
Dell? LOL
Myspace had quite a chunk of money too (the whole news corp behind it, to transform it to the new age entertainment money making machine) but failed too.
RIM? I can't really figure out if anybody has ever screwed up more than them. Perhaps Lehmon brothers and Bethlehem steel.
1 moment you got money. You blink, and then you don't. If you were once big, that speaks nothing about the future. You can take for reference Apple after Jobs departed from the CEO position. Talent management is what gets companies to survive through the years, not how much money they made in the past. Talented coders, designers, accountants and people like that a dime a dozen, good execs are 1 in a million.
People thinking some companies can't die because "OMG THEY GOT BILLIONS" is just stupid. Many companies that had billions died. Because of poor management. Many will in future too.