I'm not sure we can help you, if you don't have your own records.
I believe your basis can be increased, if the funds pay dividends that are reinvested in the fund, but they are also declared on your 1099-DIV and you pay tax on them, they increase your basis. (Dividends that are used to buy new shares, that are not taxed to you at the time, do not increase your basis.)
If you bought shares over several years, and you don't have records, and the broker doesn't have records, I don't know what to tell you. Seems like the broker's job to keep track, whether they used paper ledgers or computers or an abacus. I might contact whoever regulates brokers in your state, or the SEC, and try to poke them to do a better job for you.
If audited, the IRS does not have to allow any basis you can't prove, so you should at least make the best, most reasonable estimates you can, and write them down with an explanation. You can update it with better facts if you get them.
