Is your SME delivering directly to recipients' email servers, or relaying through your ISP?
If you're delivering directly, does your ISP allow you to connect to remote hosts on port 25? (test with 'telnet mail.hp.com smtp' from the SME server itself)
If you're using a smarthost, is it configured correctly? Does it require a username and password to allow relay, or not?
Are your clients configured to relay email through the SME server or through your ISP's mail server? (the SMTP proxy in 7.x will swallow all outbound smtp traffic by default).
I've got one network running SME 7.2 with a PIII / 933MHz / 256MB machine, so I would expect your hardware to be OK. I do have intermittent problems with incoming email (every few months) that go away if I disable spamassassin - but most of the time this system works just fine.
If you restored your sme from .tar files &c my first guess would be that something odd happened to the smtpd, qpsmtpd or domains configuration.
If none of these hints gets you going, we'll need to see the results of the following commands. Be sure to obfuscate any sensitive information like external IP addresses or hostnames.
config show smtpd
config show qpsmtpd
db domains show
/sbin/e-smith/audittools/newrpms