Two different messages, two different causes.
"Bandwidth limit exceeded" applies only to older plans that carried a monthly transfer allowance; all our current plans are unmetered. If you see it, the quickest fix is to upgrade to a current plan from your client area (Services → My Services → your hosting → Upgrade/Downgrade) — it's pro-rated and takes effect immediately, with no migration because you stay on the same server. If the upgrade option isn't available to you, open a ticket telling us how much traffic you're expecting and we'll sort it directly.
"This account has been suspended" is nearly always an unpaid invoice. You get three reminders first; once the invoice is paid the account comes back automatically within minutes. Check Billing → My Invoices in your client area. Very rarely it's a security suspension — a compromised site sending spam, say — in which case there'll already be a ticket from us explaining what we found and what needs to happen.
Either way, if the message doesn't match what you're seeing in your client area, open a ticket and we'll look straight away.
