I'd suggest putting together a quick little file such as:
<?
phpinfo();
?>
Run that. Then look for a section titled "session". If you find it, check if session support is enabled or disabled. If you don't find a "session" section, then that PHP install does not have sessions enabled.
If sessions are not enabled, you can use cookies with an expiration time of 0. When its zero, the cookie will be destroyed when the browser is closed, which is how sessions work. The only difference is you'll have a little more coding to do to set and retrieve the cookies.
I'd double check if sessions are enabled first. If they're disabled, I might suggest contacting your host and find out why they're disabled and see if they'll enable them (might ask them to upgrade their PHP version while they're at it).