Can I open a Traditional IRA if I have a 401(k) and a Roth IRA?

Having existing accounts would never disqualify you from opening another account type. The ability to start the new account is based on other factors. In your case it's simply a question of whether you have taxable compensation (money earned by the sweat of thy brow) which you apparently do since you have a 401(k), and have not exceeded the annual deposit limit. Thus, I expect that the first caveat is not an issue, and since you are aware you cannot deposit to the Roth this year, no deposits were made yet. In which case, you are able to make the deposit to the (new) IRA, non-deductible, wait for the money to clear, and convert it to your Roth IRA.

For those reading this. It appears that OP (original question poster) has not yet opened any Traditional IRA. If he had one already, the transfer of money from the Traditional IRA to a Roth IRA would likely trigger a tax. A prorated portion of the (previously) tax-deducted deposits to that Traditional IRA, along with the growth therefrom, would be considered to be part of the money transferred to the Roth IRA, and that prorated part would be taxable income to the IRA owner. Note that, in accordance with tax law, the IRS considers all Traditional IRA accounts (regardless of who the custodians are) to be part of the one single Traditional IRA that the owner has, and so, transfer of the money from just the Traditional IRA account just opened to the Roth IRA doesn't help in the least: the money is deemed to be from the owner's (single) Traditional IRA and is prorated and taxed as described.