Sudden white screen of death occurrence / site mostly inaccessible

Hello all,

Since yesterday morning, I experience severe "white screen of death" problems on a small Drupal 5.1 site (theme SeoPosition, shared hosting). No changes to the site have been made for quite a while. Just some small content modifications now and then. It had been working
fine since the beginning. Now, I get the white screen almost anywhere on the site, at any time, clicking on whatever link, but most especially when logging on as admin, which has become almost impossible. Striking the F5 key repeatedly eventually seems to get me there in the end. I asked the hosting if they had changed anything, but they say they haven't.

Checking my hosting's log, I find errors I never saw before :

It started with this :
PHP Fatal error: Call to undefined function is_null() in /home/httpd/vhosts/mysite.com/httpdocs/subdir/includes/bootstrap.inc on line 770, referer: http://www.mysite.com/subdir/user/1

And then follow thousands (really !) of these :
PHP Warning: htmlspecialchars() expects parameter 2 to be long, string given in /home/httpd/vhosts/mysite.com/httpdocs/subdir/includes/bootstrap.inc on line 588, referer: http://www.mysite.com/subdir/user/1

Finally concluded by some of these :
PHP Fatal error: Call to undefined function is_null() in /home/httpd/vhosts/mysite.com/httpdocs/subdir/includes/bootstrap.inc on line 770,
referer: http://www.mysite.com/subdir/admin/content/types
PHP Fatal error: Allowed memory size of 33554432 bytes exhausted (tried to allocate 2941231668 bytes) in
/home/httpd/vhosts/mysite.com/httpdocs/subdir/includes/install.inc on line 41, referer: http://www.mysite.com/subdir/user/2
PHP Fatal error: Allowed memory size of 33554432 bytes exhausted (tried to allocate 2947806512 bytes) in
/home/httpd/vhosts/mysite.com/httpdocs/subdir/includes/install.inc on line 41, referer: http://www.mysite.com/subdir/user/1
PHP Fatal error: Allowed memory size of 33554432 bytes exhausted (tried to allocate 2941251448 bytes) in
/home/httpd/vhosts/mysite.com/httpdocs/subdir/includes/install.inc on line 41, referer: http://www.mysite.com/subdir/user/1

So ... tried to allocate 2,941,231,668 bytes ???

(PHP memory = 32M but that never seemed to be a problem before).

Any suggestions would be very much appreciated.
Thank you !